Question

Simplify:
(1/2)log[3]x-2 log[3]y+4 log[3]z
Solve for x:
log[3]x-log[3]2=2

Answer 1

\[\frac{1}{2}\log_{3} x-2\log_{3} y+4\log_{3} z=\log_{3} \sqrt{x}-\log_{3} y ^{2}+\log_{3}z ^{4}\]=\[\log_{3} \frac{\sqrt{x}}{y ^{2}}\times z ^{4}\]

Answer 2

\[\log_{3} x-\log_{3} 2=2\]
\[\log_{3} \frac{x}{2}=2\]
\[3^{2}=9=\frac{x}{2}\]
x = 18