Use properties of logarithms to expand the logarithmic
expression as much as possible. Where possible, evaluate
loganthmic expressions without using a calculator.

Ask by Bowers Thornton. in the United States

Mar 23,2025

Question

Use properties of logarithms to expand the logarithmic
expression as much as possible. Where possible, evaluate
loganthmic expressions without using a calculator.

Ask by Bowers Thornton. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

We start with the given expression:
$$
\log_c x^4
$$

Using the power rule for logarithms, which states that for any positive number $$ x $$ and any real number $$ a $$,

$$
\log_b \left( x^a \right) = a\log_b x,
$$

we can apply this rule with $$ a = 4 $$ to the expression:

$$
\log_c x^4 = 4\log_c x.
$$

Thus, the expanded form is:

$$
\boxed{4\log_c x}
$$
$$ \log_c x^4 = 4\log_c x $$