Question

How would I solve for X in the below equation

4^(3x - 5) = (16)^(x+2)

preferably with steps so I can learn how to do it on my own if that's ok

Answer 1

x=9

Explanation:

4^(3x - 5) = (16)^(x+2)

Rewrite 16 as 4^2

4^(3x - 5) = 4^2^(x+2)

We know a^b^c = a^(b*c)

4^(3x - 5) = (2)^(2*(x+2))

4^(3x - 5) = (4)^(2x+4)

The bases are the same so the exponents are the same

3x-5 = 2x+4

Subtract 2x from each side

3x-5-2x = 2x+4-2x

x-5 = 4

Add 5 to each side

x-5+5 =4+5

x=9