QuestionFind $\log_{8} 1,000$ using $\ln 8 \approx 2.08$ and $\ln 1,000 \approx 6.91$ .

Studdy Solution

STEP 1

Assumptions1. We have the values $\ln8 \approx.08$ and $\ln1,000 \approx6.91$ . We need to find the approximate value of $\log{8}1,000$
3. We can use the change of base formula, which states that $\log_b a = \frac{\ln a}{\ln b}$

STEP 2

We will use the change of base formula to express $\log{8}1,000$ in terms of natural logarithms.
$\log{8}1,000 = \frac{\ln1,000}{\ln8}$

STEP 3

Now, substitute the given values for $\ln8$ and $\ln1,000$ into the formula.
$\log{8}1,000 = \frac{6.91}{2.08}$

STEP 4

Perform the division to find the approximate value of $\log{8}1,000$ .
$\log{8}1,000 \approx \frac{6.91}{2.08} \approx3.32$ So, $\log{8}1,000 \approx3.32$ .

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