Question

choose the single logarithm expression that is equivalent to the one shown 1 / 3 log 3x + 2 / 3 log 3x​

Answer 1

Answer:

$\log (3x)$

Step-by-step explanation:

The given logarithmic expression is:

$\frac{1}{3}\log(3x)+ \frac{2}{3}\log(3x)$

This is the same as:

$\frac{1}{3}\log(3x)+ \frac{1}{3}\log(3x)^2$

$\frac{1}{3}(\log(3x)+ \log(3x)^2)$

We now apply the product rule to get:

$\frac{1}{3}\log(3x)\times (3x)^2$

$\frac{1}{3}\log (3x)^3$

We now apply the power rule to get;

$\frac{3}{3}\log (3x)=\log (3x)$