Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1 . Evaluate logarithmic expressions if possible.

(Simplify your answer.)

Ask by Robbins Bowers. in the United States

Mar 23,2025

Question

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1 . Evaluate logarithmic expressions if possible.

(Simplify your answer.)

Ask by Robbins Bowers. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

We start with the expression:
$$
5 \ln x - \frac{1}{3} \ln y
$$

Using the property $$a \ln b = \ln(b^a)$$, we can rewrite each term:
$$
5 \ln x = \ln(x^5) \quad \text{and} \quad \frac{1}{3} \ln y = \ln(y^{\frac{1}{3}})
$$

Thus, the expression becomes:
$$
\ln(x^5) - \ln(y^{\frac{1}{3}})
$$

Now, applying the logarithm property $$\ln a - \ln b = \ln\left(\frac{a}{b}\right)$$, we have:
$$
\ln(x^5) - \ln(y^{\frac{1}{3}}) = \ln\left(\frac{x^5}{y^{\frac{1}{3}}}\right)
$$

Therefore, the simplified expression is:
$$
5 \ln x - \frac{1}{3} \ln y = \ln\left(\frac{x^5}{y^{\frac{1}{3}}}\right)
$$
$$ 5 \ln x - \frac{1}{3} \ln y = \ln\left(\frac{x^5}{y^{\frac{1}{3}}}\right) $$

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1 . Evaluate logarithmic expressions if possible.

(Simplify your answer.)

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Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1 . Evaluate logarithmic expressions if possible. (Simplify your answer.)

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Latest Pre Algebra Questions

Use properties of logarithms to condense the logarithmic
expression. Write the expression as a single logarithm whose
coefficient is 1 . Evaluate logarithmic expressions if possible.

(Simplify your answer.)