Write the expression as a logarithm of a single number or expression, and then simplify if possible. Enter only the simplified expression. Assume each of the given variable expressions is defined for appropriate values of the variable(s) contained in it. $$ \frac{1}{2} \log \left(4 x^{6}\right)-\log \left(x^{2}\right)= $$

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UpStudy AI · Accepted Answer

$$ \frac{1}{2} \log \left(4x^6\right) = \log \left(\left(4x^6\right)^{\frac{1}{2}}\right) = \log \left(2x^3\right) $$

Thus, the expression becomes:

$$
\log \left(2x^3\right) - \log \left(x^2\right)
$$

Using the logarithm subtraction rule:

$$
\log \left(\frac{2x^3}{x^2}\right) = \log \left(2x\right)
$$

$$ \log(2x) $$
$$ \log(2x) $$

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