SOLUTION: Solve the following exponential equation: 4^(1-3x) = 5^(0.5x+7) I have it about half way and then I'm stuck, really need to see all the steps. Thank you.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the following exponential equation: 4^(1-3x) = 5^(0.5x+7) I have it about half way and then I'm stuck, really need to see all the steps. Thank you.      Log On


   

Question 1054563: Solve the following exponential equation:
4^(1-3x) = 5^(0.5x+7)
I have it about half way and then I'm stuck, really need to see all the steps. Thank you.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Take log of both sides and change one of them using Change of Base formula.



Another way is just use log base ten.

log%2810%2C4%5E%281-3x%29%29=log%2810%2C5%5E%280.5x%2B7%29%29

%281-3x%29%2Alog%28%284%29%29=%280.5x%2B7%29log%28%285%29%29

log%28%284%29%29-3%2Alog%28%284%29%29x=0.5%2Alog%28%285%29%29x%2B7%2Alog%28%285%29%29

log%28%284%29%29=0.5%2Alog%28%285%29%29x%2B3%2Alog%28%284%29%29%2B7%2Alog%28%285%29%29

log%28%284%29%29-7%2Alog%28%285%29%29=x%280.5%2Alog%28%285%29%29%2B3%2Alog%28%284%29%29%29


Look in your reference information for those logarithms, base ten, and do the computations for x.