SOLUTION: Use algebraic procedures to find the exact solution(s) of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 4^(4x &#8722;

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Question 628010: Use algebraic procedures to find the exact solution(s) of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
4^(4x − 3) = 5^(−x − 1)
x=(?,?)
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Take the log of both sides (any base, doesn't matter)

Use on both sides

Multiply both sides by

just for the sake of neatness, let

Then it is just plain old algebra from here:

Since you want the exact answer, and you don't care about actually being able to approximate the log values, you can get a much neater answer using base 4 logs:

I'll let you figure out why these two answers are the same. Hint: What is the value of ?

John

My calculator said it, I believe it, that settles it

SOLUTION: Use algebraic procedures to find the exact solution(s) of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 4^(4x &#8722;

SOLUTION: Use algebraic procedures to find the exact solution(s) of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 4^(4x −