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\}`

Step-by-step 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=(3 \ln 4)/(2)`

Thus,
`\ln 4=\ln 2^2=2\ln 2`

Hence, the above expression becomes,

`\ln x=(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.