SOLUTION: The bases on each side of the equation cannot be made the same. Therefore, take the logarithm of each side in order to solve the equation. {{{2^(3x-4)=5}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The bases on each side of the equation cannot be made the same. Therefore, take the logarithm of each side in order to solve the equation. {{{2^(3x-4)=5}}}      Log On


   

Question 373936: The bases on each side of the equation cannot be made the same. Therefore, take the logarithm of each side in order to solve the equation.
2%5E%283x-4%29=5
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%283x-4%29=5

Take logs of both sides:

log%28%282%5E%283x-4%29%29%29=log%28%285%29%29

Use the principle of logarithms:  log%28B%2C%28A%5EC%29%29=C%2Alog%28B%2C%28A%29%29 on the left side

%283x-4%29log%28%282%29%29=log%28%285%29%29

Divide both sides by log%282%29

%283x-4%29log%28%282%29%29%2Flog%28%282%29%29%22%22=%22%22log%28%285%29%29%2Flog%28%282%29%29

3x-4%22%22=%22%22log%28%285%29%29%2Flog%28%282%29%29

Get a calculator and do the right side:


3x-4=2.321928095

Add 4 to both sides

3x=6.321928095

Divide both sides by 3

3x%2F3=6.321928095%2F3

cross%283%29x%2Fcross%283%29=6.321928095%2F3

x=6.321928095%2F3

x=2.107309365

Edwin