Question

Solve Highschool Pre cal

Answer 1

Option C:

`\ln 64 y^(2)`

Solution:

Given expression: 2 ln 8 + 2 ln y

Applying log rule
`a \log b=\log b^(a)` in the above expression.

⇒
`2 \ln 8+2 \ln y=\ln 8^(2)+\ln y^(2)`

Applying log rule
`\log a+\log b=\log (a b)` in the above expression.

⇒
`\ln 8^(2)+\ln y^(2)=\ln \left(8^(2) y^(2)\right)`

We know that
`8^(2)=64`

⇒
`\ln \left(8^(2) y^(2)\right)=\ln 64 y^(2)`

Hence, the expression in single natural logarithm is
`\ln 64 y^(2)`.