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.

Step-by-step explanation:

It is given that,

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

That implies,

Since

`\text{ log}a-\text{ log}b=\text{ log}((a)/(b))`

Then,

`\begin{gathered} \text{ log}(4)-\text{ log}(400,000)=\text{ log}((4)/(400,000)) \\ =\text{ log}((1)/(100,000)) \\ =\text{ log}((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.