Question

How do you solve `2^x * 4^(x+5)=4^(2x-1)`?

Answer 1

x=12

Explanation:

Rewrite the equation with all the exponents with the same base, which would obviously 2.

`2^x * (2^2)^(x+5)= (2^2)^(2x-1)`

`2^x * 2^(2x+10) = 2^(4x-2)`

`2^(3x+10)=2^(4x-2)`

Since base is same on both sides, equate the exponents 3x+10=4x-2 and solve for x.

x=12