Question

38. Write each logarithm as an equivalent expression involving only logarithms base 10.

b. log100(x2)

Answer 1

`\log_(100)(x^(2)) = (\log_(10)(x^(2)))/(\log_(10)(100)) = (\log_(10)(x^(2)))/(2)`

Explanation:

We can use this expression to change the base of a logarithm from b to d.

`\log_(b)(x) = (\log_(d)(x))/(\log_(d)(b))`

So, to write
`\log_(3)(25)` as base 10, we can use this formula.

`\log_(100)(x^(2)) = (\log_(10)(x^(2)))/(\log_(10)(100)) = (\log_(10)(x^(2)))/(2)`