DuckieDai Log Expander Python Program

exponential functions · MIT License

Overview

Expand the log of a product, quotient, or power into a sum of simpler logs, step by step: enter the factors on the top and bottom with their powers.

Owner-tested on a TI calculator
Version 1.0.0
2349 bytes
No imports

Download LOGEXSF.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 factor is assumed to be positive, so each log in the answer is defined.
A plain number that is a whole power of the base, such as 8 in base 2, becomes a whole number; e becomes 1 in a natural log.
Up to 12 factors on the top and 12 on the bottom.

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Learn the math

How to expand a logarithm

The idea

Expanding a log turns the log of one big expression into a sum of simpler logs. Products become sums, quotients become differences, and powers come out in front.

Write the expression as factors on the top and factors on the bottom, each with a power. Every top factor adds its log, every bottom factor subtracts its log, and each power multiplies its log.

The formula

log_b(A*B) = log_b(A) + log_b(B)

log_b(A/B) = log_b(A) - log_b(B)

log_b(A^p) = p*log_b(A)

log_b(b^k) = k

b: the base: Enter for 10, a number such as 2, or a letter. Choose ln for base e
A, B: the factors, each assumed positive
p: the power of a factor; a square root is the power 1/2

Using the program

Choose 1 for log or 2 for ln. For log, type the base, or press enter for base 10.
Say how many factors are on the top, then type each factor and its power. Press enter for a power of 1.
Do the same for the bottom; type 0 if there is no bottom.
Type a factor with brackets, such as (x+1), to keep it together. The brackets are dropped in the answer: log(x+1).
Plain numbers that are exact powers of the base, such as 8 in base 2 or e in ln, become whole numbers.

Worked example

Expand log(x^2 y^3 / z). Choose 1 and press enter for base 10. Top: 2 factors, x with power 2 and y with power 3. Bottom: 1 factor, z with power 1.

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

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

Expand ln(e^2 sqrt(x)). Choose 2. Top: 2 factors, e with power 2 and x with power 1/2. Bottom: 0. The program shows 2 + 1/2*ln(x), because ln(e^2) is 2.

Expand log_2(8x). Choose 1 with base 2. Top: 8 and x, both with power 1. Bottom: 0. The program shows 3 + log_2(x), because 2^3 = 8.

Tips and common mistakes

A log of a sum does not split: log(x + 1) stays as it is. That is why a factor like (x+1) is entered as one piece.
Rewrite roots as powers first: the cube root of x is x to the power 1/3.
Expanding assumes every factor is positive. Check that against the original problem.

Where this comes up

Expanding logarithms is a core skill in the logarithmic functions unit of algebra 2, precalculus, and college algebra, and it comes back in calculus for logarithmic differentiation.

Go further: Logarithm Rules and How to Solve Exponential Equations

Exact reviewed bytes

Source code

Download .py

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

# DuckieDai(TM) Guided Log Expand
# Assumes positive variable factors

def number(s):
 try:
  if '/' in s:
   a,b=s.split('/')
   return float(a)/float(b)
  return float(s)
 except:return None

def fmt(x):
 if abs(x-round(x))<1e-9:return str(int(round(x)))
 for d in range(2,65):
  n=round(x*d)
  if abs(x-n/d)<1e-8:return str(n)+'/'+str(d)
 return str(round(x,5))

def exact(n,b):
 if n==1:return 0
 if b is None or n<=0:return None
 v=1
 for k in range(1,21):
  v*=b
  if abs(v-n)<1e-8:return k
  if v>n:break
 return None

def term(a,p):
 if a=='e' and L=='ln':return p,''
 n=number(a)
 if n is not None:
  if n<=0:return None
  if n==1:return 0,''
  k=exact(n,B)
  if k is not None:return p*k,''
 if a.startswith('(') and a.endswith(')'):a=a[1:-1]
 return p,a

def clear():
 print('\n'*8)

def run():
 parts=[]
 for sign,name in ((1,'TOP'),(-1,'BOTTOM')):
  clear()
  print(name+' FACTORS')
  while 1:
   try:
    count=int(input('How many? '))
    if 0<=count<=12:break
   except:pass
   print('Enter 0 to 12')
  for i in range(count):
   clear()
   print(name+' '+str(i+1)+'/'+str(count))
   a=input('Factor? ').strip()
   if not a:return 'Empty factor'
   clear()
   print(name+' '+str(i+1)+'/'+str(count))
   print('SQRT = power 1/2')
   while 1:
    p=number(input('Power? (Enter=1) ') or '1')
    if p is not None and p>0:break
    print('Power must be > 0')
   t=term(a,sign*p)
   if t is None:return 'Factor must be > 0'
   parts.append(t)
 out=''
 for p,a in parts:
  if abs(p)<1e-9:continue
  w=abs(p)
  s=fmt(w) if not a else ('' if w==1 else fmt(w)+'*')+L+'('+a+')'
  if out:out+=(' + ' if p>0 else ' - ')+s
  else:out=('-' if p<0 else '')+s
 return out or '0'

print('DUCKIEDAI(TM)')
print('LOG EXPAND')
print('      __')
print('  ___(o )> quack!')
print('  \\ <_. )')
print("   `---'")
print('by DuckieDai')
print('hiddenwordscanner.com')
while 1:
 print('\n1: log  2: ln  3: quit')
 c=input('Choice? ')
 if c=='3':break
 if c not in ('1','2'):continue
 L='log' if c=='1' else 'ln'
 B=None
 if c=='1':
  b=input('Base (Enter=10)? ').strip() or '10'
  B=number(b)
  if B is not None and (B<=0 or B==1):
   print('Bad base');continue
  if B is None and not b.isalpha():
   print('Use base # or letter');continue
  if b!='10':L='log_'+b
 clear()
 answer=run()
 clear()
 print('RESULT:')
 print(answer)
 input('Press enter ')
 clear()

# DuckieDai(TM) Guided Log Expand
# Assumes positive variable factors
def number(s):
try:
if '/' in s:
a,b=s.split('/')
return float(a)/float(b)
return float(s)
except:return None
def fmt(x):
if abs(x-round(x))<1e-9:return str(int(round(x)))
for d in range(2,65):
n=round(x*d)
if abs(x-n/d)<1e-8:return str(n)+'/'+str(d)
return str(round(x,5))
def exact(n,b):
if n==1:return 0
if b is None or n<=0:return None
v=1
for k in range(1,21):
v*=b
if abs(v-n)<1e-8:return k
if v>n:break
return None
def term(a,p):
if a=='e' and L=='ln':return p,''
n=number(a)
if n is not None:
if n<=0:return None
if n==1:return 0,''
k=exact(n,B)
if k is not None:return p*k,''
if a.startswith('(') and a.endswith(')'):a=a[1:-1]
return p,a
def clear():
print('\n'*8)
def run():
parts=[]
for sign,name in ((1,'TOP'),(-1,'BOTTOM')):
clear()
print(name+' FACTORS')
while 1:
try:
count=int(input('How many? '))
if 0<=count<=12:break
except:pass
print('Enter 0 to 12')
for i in range(count):
clear()
print(name+' '+str(i+1)+'/'+str(count))
a=input('Factor? ').strip()
if not a:return 'Empty factor'
clear()
print(name+' '+str(i+1)+'/'+str(count))
print('SQRT = power 1/2')
while 1:
p=number(input('Power? (Enter=1) ') or '1')
if p is not None and p>0:break
print('Power must be > 0')
t=term(a,sign*p)
if t is None:return 'Factor must be > 0'
parts.append(t)
out=''
for p,a in parts:
if abs(p)<1e-9:continue
w=abs(p)
s=fmt(w) if not a else ('' if w==1 else fmt(w)+'*')+L+'('+a+')'
if out:out+=(' + ' if p>0 else ' - ')+s
else:out=('-' if p<0 else '')+s
return out or '0'
print('DUCKIEDAI(TM)')
print('LOG EXPAND')
print(' __')
print(' ___(o )> quack!')
print(' \\ <_. )')
print(" `---'")
print('by DuckieDai')
print('hiddenwordscanner.com')
while 1:
print('\n1: log 2: ln 3: quit')
c=input('Choice? ')
if c=='3':break
if c not in ('1','2'):continue
L='log' if c=='1' else 'ln'
B=None
if c=='1':
b=input('Base (Enter=10)? ').strip() or '10'
B=number(b)
if B is not None and (B<=0 or B==1):
print('Bad base');continue
if B is None and not b.isalpha():
print('Use base # or letter');continue
if b!='10':L='log_'+b
clear()
answer=run()
clear()
print('RESULT:')
print(answer)
input('Press enter ')
clear()

Filename: LOGEXSF.py
Size: 2349 bytes
SHA-256: d99b1ae3aaf075876819d85d042e57ef7b347db276d647274f6b4b7076cd46e5

Usage

Inputs

1 for log or 2 for ln, then for log a base (a number or a letter; Enter for 10)
How many factors are on the top and on the bottom
Each factor, such as x, (x+1), or 8, and its power

Outputs

The expanded expression, such as 2*log(x) + 3*log(y) - log(z)
Whole numbers in place of logs of exact powers of the base

Units: Pure expressions; no units.

Assumptions and limitations

Assumptions

Every variable factor is assumed to be positive, so each log in the answer is defined.
A plain number that is a whole power of the base, such as 8 in base 2, becomes a whole number; e becomes 1 in a natural log.

Constraints

Up to 12 factors on the top and 12 on the bottom.
Each power must be greater than 0; type 1/2 for a square root. Numbers may be typed as decimals or fractions.

Known failures

The program expands only; it does not simplify a log of the base itself, such as log_x(x), to 1.
A power typed as inf stops the program with an error when the result is shown.

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 the standard DuckieDai opening screen with the website line replaced the original two line title. The steps after the opening screen are unchanged; this exact file has not yet been rerun on a calculator.
Dependencies: No imports
Suggested calculator name: LOGEXSF — 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 LOGEXSF 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 2026-10-12. Download this reviewed version

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