SOLUTION: Solve for x: {{{4^x+5=12}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve for x: {{{4^x+5=12}}}      Log On


   

Question 130663: Solve for x:

4%5Ex%2B5=12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%5Ex%2B5=12 Start with the given equation.


4%5Ex=7 Subtract 5 from both sides


log%2810%2C%284%5Ex%29%29=log%2810%2C%287%29%29 Take the log of both sides


x%2Alog%2810%2C%284%29%29=log%2810%2C%287%29%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


x=log%2810%2C%287%29%29%2Flog%2810%2C%284%29%29 Divide both sides by log%2810%2C%284%29%29


x=log%284%2C%287%29%29 Use the change of base formula to simplify the right side