DuckieDai Log Properties Python Program

exponential functions · MIT License

Overview

Expand a log of a product, quotient, power, or root into simpler logs, or condense a sum of logs back into a single log, in log, a chosen base, or ln.

Owner-tested on a TI calculator
Version 1.0.0
2851 bytes
Uses math

Download LOGPROPU.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer to the Python App; the owner's transfer details were not recorded
Every variable is assumed to be positive, so each log is defined.
Products are written with *, and sqrt( ) counts as a power of 1/2.
A sum or difference inside the log, such as x+1, is kept whole, because the log of a sum cannot be split.

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Learn the math

How to expand and condense logarithms

The idea

A logarithm turns multiplication into addition. Because of that, the log of a product, quotient, or power can be split into a sum of simpler logs, called expanding, and a sum of logs with numbers in front can be packed back into one log, called condensing.

Expanding helps when you need to differentiate or simplify; condensing helps when you solve an equation, because one log on each side can be undone. The same three rules work for log, ln, and a log in any base.

The formula

log(xy) = log(x) + log(y)

log(x/y) = log(x) - log(y)

log(x^n) = n log(x)

product rule: the log of a product is the sum of the logs
quotient rule: the log of a quotient is the log of the top minus the log of the bottom
power rule: a power inside a log moves to the front as a number; a square root is the power 1/2

Using the program

Choose 1 to expand or 2 to condense, then 1 for log, 2 for a base you choose, or 3 for ln.
To expand, type what is inside the log with * for multiplication, such as (x^3*y^2)/z^4. sqrt( ) counts as a power of 1/2.
To condense, type how many terms there are, then for each term its number in front, such as 2 or -1, and what is inside its log.
A number that is an exact power of the base, such as 8 in base 2, becomes a whole number in the answer.

Worked example

Expand log((x^3*y^2)/z^4). Choose 1, then 1 for log, and type (x^3*y^2)/z^4.

log(x^3) + log(y^2) - log(z^4) = 3log(x) + 2log(y) - 4log(z)

The program shows RESULT: 3log(x) + 2log(y) - 4log(z).

Expand log_2(8x/sqrt(y)). Choose 1, then 2, base 2, and type 8*x/sqrt(y). log_2(8) is 3, so the program shows 3 + log_2(x) - (1/2)log_2(y).

Condense 2ln(x) + 3ln(y) - ln(z). Choose 2, then 3 for ln, type 3 terms, then 2 and x, 3 and y, and -1 and z. The program shows ln((x^2*y^3)/z).

Tips and common mistakes

There is no rule for the log of a sum: log(x+1) cannot be split, so the program keeps it whole.
Every variable is assumed to be positive, so each log in the answer is defined.
Write products with *: 2x is read as a single factor, while 2*x is split into log(2) + log(x).
When condensing, a negative number in front sends that factor to the bottom of the fraction.

Where this comes up

The properties of logarithms are a core part of the logarithmic functions unit of algebra 2, precalculus, and college algebra, and calculus uses them for logarithmic differentiation.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

from math import log
def P(s):print(s);input("[enter]");print("\n"*11)
def fmt(v):
 if abs(v-round(v))<1e-9:return str(int(round(v)))
 for d in range(2,101):
  n=round(v*d)
  if abs(v-n/d)<1e-8:return str(n)+"/"+str(d)
 return str(round(v,6))
def st(s):
 while s[:1]=="(" and s[-1:]==")":
  d=0
  for i in range(len(s)):
   d+=(s[i]=="(")-(s[i]==")")
   if d<1 and i<len(s)-1:return s
  s=s[1:-1]
 return s
def sp(s,o):
 r=[];l=0;d=0
 for i in range(len(s)):
  c=s[i];d+=(c=="(")-(c==")")
  if d==0 and c in o and i>l:r+=[s[l:i],c];l=i+1
 return r+[s[l:]]
def val(s):
 s=st(s)
 if "/" in s:a,b=s.split("/");v=float(a)/float(b)
 else:v=float(s)
 if v-v:raise ValueError("Not a number")
 return v
def bi(s):
 d=0
 for i in range(len(s)):
  c=s[i];d+=(c=="(")-(c==")")
  if d==0 and i and c in"+-" and s[i-1] not in"^*/(" and not(i>1 and s[i-1] in"eE" and s[i-2] in"0123456789."):return 1
 return 0
def at(s,c=1):
 s=st(s)
 if bi(s):return [(s,c)]
 p=sp(s,"*/")
 if len(p)>1:
  r=[];g=1
  for q in p:
   if q=="*":g=1
   elif q=="/":g=-1
   else:r+=at(q,c*g)
  return r
 p=sp(s,"^")
 if len(p)==3:return at(p[0],c*val(p[2]))
 if s[:5]=="sqrt(" and s[-1:]==")":return at(s[5:-1],c/2)
 if not s:raise ValueError("Missing factor")
 return [(s,c)]
def ex(s,L,b):
 k=0;T={};O=[]
 for t,c in at(s.replace(" ","")):
  try:
   n=val(t)
   if b:
    e=round(log(n)/log(b))
    if abs(b**e-n)<1e-8*max(1,n):k+=c*e;continue
  except Exception:pass
  if t not in T:O.append(t);T[t]=0
  T[t]+=c
 o=fmt(k) if abs(k)>1e-10 else ""
 for t in O:
  c=T[t]
  if abs(c)<1e-9:continue
  f=fmt(abs(c));v=("" if f=="1" else "("+f+")" if "/" in f else f)+L+"("+t+")"
  o+=((" - " if c<0 else " + ")+v) if o else ("-" if c<0 else "")+v
 return o or "0"
def cn(L):
 n=int(input("# of terms? "));t=[];u=[]
 for i in range(n):
  c=val(input("Term "+str(i+1)+" coef? "));a=input(" Inside? ").strip()
  if not a or c==0:continue
  p=a if not any(h in a for h in "+-*/^") else "("+a+")"
  f=fmt(abs(c))
  if abs(c)!=1:p+="^"+("("+f+")" if "/" in f else f)
  (t if c>0 else u).append(p)
 s="*".join(t) or "1"
 if u:s=(s if len(t)<2 else "("+s+")")+"/"+(u[0] if len(u)<2 else "("+"*".join(u)+")")
 return L+"("+s+")"
def ch():
 while 1:
  c=input("1 log  2 log_b  3 ln? ").strip()
  if c=="1":return "log",10
  if c=="3":return "ln",None
  if c=="2":
   try:
    b=val(input("Base? "))
    if b>0 and b!=1:f=fmt(b);return "log_"+("("+f+")" if "/" in f else f),b
   except Exception:pass
   print("Base >0, not 1")
P("DuckieDai TM\nLOG PROPERTIES\n   __(o )> quack!\nhiddenwordscanner.com")
while 1:
 c=input("1 Expand 2 Condense\n3 Quit? ").strip()
 if c=="3":break
 if c not in("1","2"):continue
 L,b=ch()
 try:
  if c=="1":print("Use * : (x^3*y^2)/z^4");a=ex(input("Inside log? "),L,b)
  else:a=cn(L)
  print("\n"*11);P("RESULT:\n"+a)
 except Exception as e:P("INPUT ERROR:\n"+str(e))

from math import log
def P(s):print(s);input("[enter]");print("\n"*11)
def fmt(v):
if abs(v-round(v))<1e-9:return str(int(round(v)))
for d in range(2,101):
n=round(v*d)
if abs(v-n/d)<1e-8:return str(n)+"/"+str(d)
return str(round(v,6))
def st(s):
while s[:1]=="(" and s[-1:]==")":
d=0
for i in range(len(s)):
d+=(s[i]=="(")-(s[i]==")")
if d<1 and i<len(s)-1:return s
s=s[1:-1]
return s
def sp(s,o):
r=[];l=0;d=0
for i in range(len(s)):
c=s[i];d+=(c=="(")-(c==")")
if d==0 and c in o and i>l:r+=[s[l:i],c];l=i+1
return r+[s[l:]]
def val(s):
s=st(s)
if "/" in s:a,b=s.split("/");v=float(a)/float(b)
else:v=float(s)
if v-v:raise ValueError("Not a number")
return v
def bi(s):
d=0
for i in range(len(s)):
c=s[i];d+=(c=="(")-(c==")")
if d==0 and i and c in"+-" and s[i-1] not in"^*/(" and not(i>1 and s[i-1] in"eE" and s[i-2] in"0123456789."):return 1
return 0
def at(s,c=1):
s=st(s)
if bi(s):return [(s,c)]
p=sp(s,"*/")
if len(p)>1:
r=[];g=1
for q in p:
if q=="*":g=1
elif q=="/":g=-1
else:r+=at(q,c*g)
return r
p=sp(s,"^")
if len(p)==3:return at(p[0],c*val(p[2]))
if s[:5]=="sqrt(" and s[-1:]==")":return at(s[5:-1],c/2)
if not s:raise ValueError("Missing factor")
return [(s,c)]
def ex(s,L,b):
k=0;T={};O=[]
for t,c in at(s.replace(" ","")):
try:
n=val(t)
if b:
e=round(log(n)/log(b))
if abs(b**e-n)<1e-8*max(1,n):k+=c*e;continue
except Exception:pass
if t not in T:O.append(t);T[t]=0
T[t]+=c
o=fmt(k) if abs(k)>1e-10 else ""
for t in O:
c=T[t]
if abs(c)<1e-9:continue
f=fmt(abs(c));v=("" if f=="1" else "("+f+")" if "/" in f else f)+L+"("+t+")"
o+=((" - " if c<0 else " + ")+v) if o else ("-" if c<0 else "")+v
return o or "0"
def cn(L):
n=int(input("# of terms? "));t=[];u=[]
for i in range(n):
c=val(input("Term "+str(i+1)+" coef? "));a=input(" Inside? ").strip()
if not a or c==0:continue
p=a if not any(h in a for h in "+-*/^") else "("+a+")"
f=fmt(abs(c))
if abs(c)!=1:p+="^"+("("+f+")" if "/" in f else f)
(t if c>0 else u).append(p)
s="*".join(t) or "1"
if u:s=(s if len(t)<2 else "("+s+")")+"/"+(u[0] if len(u)<2 else "("+"*".join(u)+")")
return L+"("+s+")"
def ch():
while 1:
c=input("1 log 2 log_b 3 ln? ").strip()
if c=="1":return "log",10
if c=="3":return "ln",None
if c=="2":
try:
b=val(input("Base? "))
if b>0 and b!=1:f=fmt(b);return "log_"+("("+f+")" if "/" in f else f),b
except Exception:pass
print("Base >0, not 1")
P("DuckieDai TM\nLOG PROPERTIES\n __(o )> quack!\nhiddenwordscanner.com")
while 1:
c=input("1 Expand 2 Condense\n3 Quit? ").strip()
if c=="3":break
if c not in("1","2"):continue
L,b=ch()
try:
if c=="1":print("Use * : (x^3*y^2)/z^4");a=ex(input("Inside log? "),L,b)
else:a=cn(L)
print("\n"*11);P("RESULT:\n"+a)
except Exception as e:P("INPUT ERROR:\n"+str(e))

Filename: LOGPROPU.py
Size: 2851 bytes
SHA-256: 7e06684afae5a8f5adeafffa3cd173dbdcc61bb92b6715b16c642542995a145d

Usage

Inputs

1 to expand or 2 to condense
The log: 1 log, 2 log with a base you choose, or 3 ln
To expand, what is inside the log, written with * and / such as (x^3*y^2)/z^4
To condense, how many terms, then each term's number in front and what is inside

Outputs

The expanded expression, such as 3log(x) + 2log(y) - 4log(z)
The condensed single log, such as log(x^3/y^2)
Whole numbers in place of logs of exact powers of the base, such as 3 for log_2(8)

Units: Pure expressions; no units.

Assumptions and limitations

Assumptions

Every variable is assumed to be positive, so each log is defined.
Products are written with *, and sqrt( ) counts as a power of 1/2.

Constraints

A sum or difference inside the log, such as x+1, is kept whole, because the log of a sum cannot be split.
Numbers may be decimals or fractions such as 1/2; a base must be greater than 0 and not 1.

Known failures

Two factors written side by side without *, such as 2x, are treated as one factor.
Typing something other than a whole number for the number of terms shows INPUT ERROR with Python's own message.

Compatibility and review

Review status: Owner-tested on a TI calculator
Tested on: Owner reports personally running this program on a TI-84 Plus CE Python calculator; the test date, OS version, and Python App version were not recorded
What happened: Owner reported pass on the calculator before two fixes: a sum or difference inside the log, such as x+1*y, is now kept whole instead of being split at the *, which gave a wrong answer, and inf or nan typed as a number now shows INPUT ERROR: Not a number. Every other step is unchanged; this exact file has not yet been rerun on a calculator.
Dependencies: math
Suggested calculator name: LOGPROPU — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as LOGPROPU or another name, then open the Python App and try the worked example on this page first. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-10-22. Download this reviewed version

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