Use properties of logarithms to evaluate the expression.

Ask by Nguyen Ayala. in the United States

Jan 24,2025

Question

Use properties of logarithms to evaluate the expression. $$ \ln e^{9}-\ln e^{8}+\ln e^{6} $$

UpStudy AI · Accepted Answer

To evaluate the expression $$ \ln e^{9} - \ln e^{8} + \ln e^{6} $$, we can use the properties of logarithms, specifically:

1. **Power Rule of Logarithms**: $$ \ln e^x = x $$ because the natural logarithm ($$ \ln $$) and the exponential function ($$ e^x $$) are inverses of each other.

Let's apply this property to each term in the expression:

1. $$ \ln e^{9} = 9 $$
2. $$ \ln e^{8} = 8 $$
3. $$ \ln e^{6} = 6 $$

Now, substitute these values back into the original expression:

$$
\ln e^{9} - \ln e^{8} + \ln e^{6} = 9 - 8 + 6 = 7
$$

**Final Answer:** $$ 7 $$
$$ 7 $$

Use properties of logarithms to evaluate the expression.

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