Question

Given that log_{a}(3) = 0.477 and

Answer 1

Given:

$\log_{a}(3) = 0.477,\log_{a}(5) = 0.699$

To find:

The value of $\log_{a}(0.6)$.

Solution:

We need to find the value of:

$\log_{a}(0.6)$

It can be written as

$\log_{a}(0.6)=\log_a\left(\dfrac{6}{10}\right)$

$\log_{a}(0.6)=\log_a\left(\dfrac{3}{5}\right)$

By using the property of logarithm, we get

$\log_{a}(0.6)=\log_a(3)-\log_a(5)$        $[\because \log \dfrac{a}{b}=\log a-\log b]$

$\log_{a}(0.6)=\log_a(3)-\log_a(5)$

On substituting the given values, we get

$\log_{a}(0.6)=0.477-0.699$

$\log_{a}(0.6)=-0.222$

Therefore, the values of $\log_a(0.6)$ is -0.222.