Question

Identify the solution set of 3 In 4 = 2 In x. -{6} -{-8,8} -(8)

Answer 1

Option C: The solution set is $\{8\}$

Explanation:

The expression is $3 \ln 4=2 \ln x$

Now, let us find the solution set.

Switch sides, we get,

$2 \ln x=3 \ln 4$

Dividing by 2 on both sides, we have,

$\ln x=\frac{3 \ln 4}{2}$

Thus,  $\ln 4=\ln 2^2=2\ln 2$

Hence, the above expression becomes,

$\ln x=\frac{3 \cdot 2 \ln (2)}{2}$

Simplifying, we get,

$\ln x=3 \ln 2$

Applying the log rule, we get,

$\ln x =\ln \left(2^{3}\right)$

Simplifying, we have,

$\ln x =\ln \left8\right$

Applying the log rule, we have,

$x=8$

Thus, the solution set is $\{8\}$

Hence, Option C is the correct answer.