SOLUTION: I need help with this problem: Find the solution using common logarithms, and two-decimal-place approximation of the solution. 4^x - 3(4^-x) = 8 Thank you!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I need help with this problem: Find the solution using common logarithms, and two-decimal-place approximation of the solution. 4^x - 3(4^-x) = 8 Thank you!      Log On


   

Question 880340: I need help with this problem:
Find the solution using common logarithms, and two-decimal-place approximation of the solution.
4^x - 3(4^-x) = 8
Thank you!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The equation can take a quadratic form.
Let u=4%5Ex, and solve this for u, first.

Skipping the substitution and the show of steps,....
u%5E2-8u-3=0,...

4%5Ex=%288%2B-+3sqrt%286%29%29%2F2-----Can you continue and finish from here?

Taking logs of both sides and solve for x, solutions before making the approximations:

highlight%28x=log%28%28%288-3sqrt%286%29%29%2F2%29%29%2Flog%28%284%29%29%29 OR highlight%28x=log%28%28%288%2B3sqrt%286%29%29%2F2%29%29%2Flog%28%284%29%29%29