Suppose 2^x = 10.

Compute 8^x

i get 8 ^((ln 10) / (ln 2) ) but this was incorrect? i do think it was right, ideas or something im missing?

3 answers

8 = 2^3

(2^3)^x = (2^x)^3 = 10^3
recall how to change base of logs.
8 ^((ln 10) / (ln 2) ) = 8^log210
= (2^3)^210
= 2^(210)^3
But, 2^210 = 10
so, it's still 10^3
2^x = 10.
x*Log2 = Log10,
X = Log10/Log2 = 3.32192809.

8^x = 8^(3.32192809) = 1000.