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=(\log_(10)0.877)/(\log_(10)9)`
`[\because \log_yx=(\log_ax)/(\log_ay)]`

`\log_90.877=(-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.