Use the change-of-base formula to evaluate . Round your answer to the nearest thousandth.

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Ask by Santiago Brooks. in the United States

Mar 27,2025

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Use the change-of-base formula to evaluate $$ \log _{4} 7 $$. Round your answer to the nearest thousandth. $$ \log _{4} 7 \approx \square $$ U Listen Provious

UpStudy AI · Accepted Answer

To evaluate $$ \log_{4} 7 $$ using the change-of-base formula, we can use the formula:

$$ \log_{a} b = \frac{\log_{c} b}{\log_{c} a} $$

where $$ a $$, $$ b $$, and $$ c $$ are positive real numbers and $$ c \neq 1 $$.

In this case, we want to find $$ \log_{4} 7 $$, so we can use the change-of-base formula with $$ a = 4 $$, $$ b = 7 $$, and $$ c = 10 $$ (since we are using the common logarithm).

$$ \log_{4} 7 = \frac{\log_{10} 7}{\log_{10} 4} $$

Now, we can calculate the values of $$ \log_{10} 7 $$ and $$ \log_{10} 4 $$ and then divide them to find $$ \log_{4} 7 $$.

Let's calculate the values:

$$ \log_{10} 7 \approx 0.8451 $$
$$ \log_{10} 4 \approx 0.6021 $$

Now, we can divide these values to find $$ \log_{4} 7 $$:

$$ \log_{4} 7 = \frac{0.8451}{0.6021} \approx 1.404 $$

Therefore, $$ \log_{4} 7 \approx 1.404 $$ when rounded to the nearest thousandth.
$$ \log_{4} 7 \approx 1.404 $$

Use the change-of-base formula to evaluate . Round your answer to the nearest thousandth.

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Use the change-of-base formula to evaluate . Round your answer to the nearest thousandth. U Listen Provious