Question

PLEASE HELP !!!!!!!!!

Answer 1

`\log_2{\left((x^2z)/(y^2)\right)}+\log_9{(x^(12)y^4)}`

Explanation:

The appropriate rules of logarithms are ...

log(a)+log(b) = log(ab)

n·log(a) = log(a^n)

We can use these rules to combine the logs to the same base so each is a log of a single expression.

`\log_2{z}+2\log_2{x}+4\log_9{y}+12\log_9{x}-2\log_2{y}\\\\=\log_2{(z\cdot x^(2)\cdot y^(-2))}+\log_9{(y^(4)\cdot x^(12))}\\\\=\log_2{\left((x^2z)/(y^2)\right)}+\log_9{(x^(12)y^4)}`