Question

Evaluate log_4(1/cuberoot(16))

Answer 1

\[\log_{4} \sqrt[3]{16}= ?\]

Answer 2

I feel I have to use log_bB^x=x, but I just can't get it.
The answer is supposed to be -2/3.
But as far as I've gotten is:
log_4(16^-1/3) and i have the feeling I should put 16 as 4^2.. but something just doesn't work out

Answer 3

\[\log_{b^n}a^m=\frac{ m }{ n } \log_{b} a\]

Answer 4

@amoodarya yes exactly that

Answer 5

@amoodarya How would I apply it? I see the base is raised to the n power, do i make it a 2^2?

Answer 6

\[\sqrt[3]{16}=2^{\frac{ 4 }{ 3 }}\]

Answer 7

\[\log_{4} \frac{1}{\sqrt[3]{16}}=x\\4^x=\frac{1}{\sqrt[3]{16}}\\2^{2x}=2^{\frac{ -4 }{ 3 }}\\2x=\frac{ -4 }{ 3 }\]

Answer 8

Thanks for the help!