Question

What is 2logs(5x°)+ logs(+6) written as a
single logarithm?

Answer 1

Given:

The expression is:

`2\log_5(5x^3)+(1)/(3)\log_5(x^2+6)`

To find:

The single logarithm expression for the given expression.

Solution:

We have,

`2\log_5(5x^3)+(1)/(3)\log_5(x^2+6)`

Using properties of the logarithm, we get

`=\log_5(5x^3)^2+\log_5(x^2+6)^{(1)/(3)}`
`[\because \log x^n=n\log x]`

`=\log_5(25x^6)+\log_5\sqrt[3]{x^2+6}`

`=\log_5(25x^6)\sqrt[3]{x^2+6}`
`[\because \log a+\log b=\log (ab)]`

Therefore, the correct option is B.