Option C: The solution set is [tex]\{8\}[/tex]
Explanation:
The expression is [tex]3 \ln 4=2 \ln x[/tex]
Now, let us find the solution set.
Switch sides, we get,
[tex]2 \ln x=3 \ln 4[/tex]
Dividing by 2 on both sides, we have,
[tex]\ln x=\frac{3 \ln 4}{2}[/tex]
Thus, [tex]\ln 4=\ln 2^2=2\ln 2[/tex]
Hence, the above expression becomes,
[tex]\ln x=\frac{3 \cdot 2 \ln (2)}{2}[/tex]
Simplifying, we get,
[tex]\ln x=3 \ln 2[/tex]
Applying the log rule, we get,
[tex]$\ln x$=\ln \left(2^{3}\right)$[/tex]
Simplifying, we have,
[tex]$\ln x$=\ln \left8\right$[/tex]
Applying the log rule, we have,
[tex]x=8[/tex]
Thus, the solution set is [tex]\{8\}[/tex]
Hence, Option C is the correct answer.
