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

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What is R?

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- np_rtLv 41 decade agoFavorite Answer
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

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- ComoLv 71 decade ago
8^r = 256

Take log base 2 of both sides:-

r log 8 = log 256

3 r = 8

r = 8 / 3

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