Question

Some help me with this please!!

Answer 1

First of all observe that

`r^6s^3=(r^2s)^3 \implies \sqrt[3]{r^6s^3}=\sqrt[3]{(r^2s)^3}=r^2s`

So, we have

`\log(r^5s^6\sqrt[3]{r^6s^3})=\log(r^5s^6\cdot r^2s)`

We can simplify the input as

`\log(r^5s^6\cdot r^2s)=\log(r^7s^7)`

The logarithm of a multiplication is the sum of the logarithms:

`\log(r^7s^7)=\log(r^7)+\log(s^7)`

Finally, invoke the logarithm property
`\log(a^b)=b\log(a)`

to get the final answer

`\log(r^7)+\log(s^7)=7\log(r)+7\log(s)`