Question

Use the change of base rule to find the logarithm to four decimal places. (2 points) log base nine of 0.877.

Answer 1

Given:

The value is $\log_90.877$.

To find:

The logarithm to four decimal places using the change of base rule.

Solution:

We have,

$\log_90.877$

Using the change of base rule, we get

$\log_90.877=\dfrac{\log_{10}0.877}{\log_{10}9}$      $[\because \log_yx=\dfrac{\log_ax}{\log_ay}]$

$\log_90.877=\dfrac{-0.057000}{0.9542425}$

$\log_90.877=-0.0597332439081$

Round the value to the four decimal places.

$\log_90.877\approx -0.0597$

Therefore, the required value is -0.0597.