Question

Plz help me solve this pre calc problem, I have to condense using the properties of log

Answer 1

Given:

`\log \left(x^(2)\right)+\log \sqrt{x^(3)+1}`

To find:

The condense of the logarithmic function.

Solution:

`\log \left(x^(2)\right)+\log \sqrt{x^(3)+1}`

Apply log rule:

`\log _(c)(a)+\log _(c)(b)=\log _(c)(a b)`

Using the log rule:

`\log _(10)\left(x^(2)\right)+\log _(10)(\sqrt{x^(3)+1})=\log _(10)\left(x^(2) \sqrt{x^(3)+1}\right)`

`\log \left(x^(2)\right)+\log \sqrt{x^(3)+1}=\log \left(x^(2) \sqrt{x^(3)+1}\right)`