Question

Need help with the question on the photo I’ve gotten it wrong multiple times not sure what

Answer 1

Given

The expression,

$\text{ log}(4)-\text{ log}(400,000)$

To find: The value.

Explanation:

It is given that,

$\text{ log}(4)-\text{ log}(400,000)$

That implies,

Since

$\text{ log}a-\text{ log}b=\text{ log}(\frac{a}{b})$

Then,

$\begin{gathered} \text{ log}(4)-\text{ log}(400,000)=\text{ log}(\frac{4}{400,000}) \\ =\text{ log}(\frac{1}{100,000}) \\ =\text{ log}(\frac{1}{10^5}) \\ =\text{ log}(10^{-5}) \end{gathered}$

Since,

$\text{ log}a^m=m\text{ log}a$

Then,

$\begin{gathered} \text{ log}(4)-\text{ log}(400,000)=\text{ log}(10^{-5}) \\ =-5\text{ log}10 \\ =-5(1) \\ =-5 \end{gathered}$

Hence, the value is -5.