Question

Janene is solving the equation log3x324=2. Which exponential equation can she use to solve the problem?

A. 324^2=3x
B. 334^x=2/3
C. (3x)^2=324
D. 3x^2=324

Answer 1

Option C: (3*x)^2 = 324

Explanation:

Janene is solving the equation:

Log₃ₓ(324) = 2

First, some rules we need to remember:

Logₙ(x) = Ln(x)/Ln(n)

and:

Ln(x^b) = b*Ln(x)

So we can rewrite our expression as:

Log₃ₓ(324) = Ln(324)/Ln(3*x) = 2

Ln(324) = 2*Ln(3*x)

Now we can use the second property:

Ln(324) = 2*Ln(3*x) = Ln( (3*x)^2 )

The arguments in both sides must be the same thing, then:

324 = (3*x)^2

This is the exponential equation she needs to solve.

Then the correct option is C.