Question

Select the correct answer.

What is the solution to this equation?
log3 (4x) – 2log3x =2

A. 36
B. 9/4
C. 4/9
D. 1/36

Answer 1

9514 1404 393

Answer:

C. 4/9

Explanation:

There are a couple of ways you can do this.

`\log_3{4x}-2\log_3{x}=2\\\\\log_3{4}+\log_3{x}-2\log_3{x}=2\\\\\log_3{4}-2=\log_3{x}\\\\4\cdot3^(-2)=x\qquad\text{take antilogs}\\\\\boxed{x=(4)/(9)}\\\\\textsf{or}\\\\(4x)/(x^2)=3^2\qquad\text{take antilogs}\\\\(4)/(9)=x\qquad\text{cancel $x$, multiply by $(x)/(9)$}`