Question

How do I simplify this​

Answer 1

x^-6

Explanation:

You want to simplify the expression 27^(-2log3(x)).

Rules of logarithms

The applicable rules of logarithms are ...

log(a^b) = b·log(a)

b^(logb(a)) = a

Application

The rewrite can proceed like this:

`27^(-2\log_3(x))=(3^3)^(-2\log_3(x))}=3^(-6\log_3(x))=3^{\log_3(x^(-6))}=\boxed{x^(-6)}`