Question

evaluate the logarithm. round your answer to the nearest thousandth. 6\log_{7}(681) \approx

Explanation:

Step1: Change log base via change of base formula

$\log_{7}(681) = \frac{\ln(681)}{\ln(7)}$

Step2: Calculate natural log values

$\ln(681) \approx 6.525$, $\ln(7) \approx 1.9459$

Step3: Compute the base-7 logarithm

$\frac{6.525}{1.9459} \approx 3.353$

Step4: Multiply by the coefficient 6

$6 \times 3.353 = 20.118$

Answer:

20.118