Question

Question #87c76

Answer 1

x = `1/2 log (50/3)`, where the logarithm is base 2.

Explanation:

`4^x` is equal to `2^(2x)`, so the equation can be written as `2^(2x)+2^(1+2x) = 50`. Factoring out `2^(2x)`, one gets `2^(2x)(1+2)=2^(2x)(3)=50`, which is equivalent to `2^(2x)=50/3`. Taking the logarithm base 2 of both sides gives `2x = log (50/3)` or, equivalently, `x = 1/2 log (50/3)`, where the logarithm is base 2.