8 to the power of r = 16 Squared, How do you solve this?

Question

What is R?

Answer 1

8^r = 16^2
(2^3)^r = (2^4)^2
2^(3r) = 2^8
3r = 8
r = 8/3


Note that you won't always be able to solve it this way to get rational numbers. Here's how you would do it in general.

8^r = 16^2 = 256
ln(8^r) = ln(256)
r*ln(8) = ln(256)
r = ln(256)/ln(8)

This is usually where it ends but in our case it can be simplified.

r = ln(2^8)/ln(2^3)
= 8*ln(2)/[3*ln(2)]
= 8/3

Answer 2

8^r = 256
Take log base 2 of both sides:-
r log 8 = log 256
3 r = 8
r = 8 / 3