Can't figure out this log problem

[dimava]

The answer is 16 but I can only get 8 when I solve it

[alkatran]

10^(x*y) = (10^x)^y
so:
10^(log10(2) * 4) = (10^log10(2))^4

x^logx(y) = y
so:
(10^log10(2))^4 = 2^4 = 16

[dimava]

thanks, I kept running in the loop of multiplying the 4*2=8

[krtxmrtz]

A similar approach based on the fact that

log(x^y) = y * log(x)

4 log₁₀(2) = log₁₀(2⁴) = log₁₀(16)

and by definition, 10^{log(something)} = something