Answer:
[tex]\log_2{\left(\dfrac{x^2z}{y^2}\right)}+\log_9{(x^{12}y^4)}[/tex]
Step-by-step 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.
[tex]\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(\dfrac{x^2z}{y^2}\right)}+\log_9{(x^{12}y^4)}[/tex]
