Question

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

Answer 1

Given:

The expression is:

$2\log_5(5x^3)+\dfrac{1}{3}\log_5(x^2+6)$

To find:

The single logarithm expression for the given expression.

Solution:

We have,

$2\log_5(5x^3)+\dfrac{1}{3}\log_5(x^2+6)$

Using properties of the logarithm, we get

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

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

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

Therefore, the correct option is B.