Question

Which equation has x=4 as the solution? A) ^log 4 (3x+4)=2 B) ^log 3 (2x-5)=2 C) ^log x 64=4 D) ^log x 16=4

Answer 1

ANSWER

$\log_{4}(3x + 4) = 2$

EXPLANATION

Consider the equation:

$\log_{4}(3x + 4) = 2$

When we rewrite this logarithmic equation in the exponential form, we obtain:

$3x + 4= {4}^{2}$

Note that to write a logarithmic equation in exponential form, the base of the logarithm is still the base in the exponential form.

We now simplify the RHS.

$3x + 4 = 16$

Group like terms

$3x = 16 - 4$

This implies that

$3x = 12$

Divide both sides by 3

$\frac{3x}{3} = \frac{12}{3}$

Simplify to get;

$x = 4$

Hence the equation that has x=4 as a solution is

$\log_{4}(3x + 4) = 2$

Another way to do this is to substitute x=4 into each equation. The equation that is satisfied is the correct choice.