Question

What is 2 log subscript 5 baseline (5 x cubed) one-third log subscript 5 baseline (x squared 6) written as a single logarithm?

Answer 1

The value of logarithm expression 2log₅(5x³) + (1/3)log₅(x² + 6) is simplified as log₅[{25x⁶}{∛(x² + 6)}].

What is a logarithm?

Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.

The logarithmic expression is given as

$2\log _55x^3 + \dfrac{1}{3} \log _5(x^2 +6)$

We know that formulas

$a \log b = \log b^a\\\\\log a + \log b = \log ab$

Then we have

$\rightarrow \log _5(5x^3)^2 + \log _5(x^2 +6)^{1/3}\\\\\rightarrow \log _525x^6 + \log _5\sqrt[3]{(x^2 +6)}\\\\\rightarrow \log _5 25x^6 (\sqrt[3]{(x^2 +6)})$

More about the logarithm link is given below.

brainly.com/question/7302008