Question

How do you rewrite `10^u = v` in logarithmic form?

Answer 1

`log_10v=u`

Explanation:

Take the base 10 logarithm of both sides

`log_10(10^u)=log_10(v)`

Using properties logarithms we can rewrite the left hand side.

`u(log_10(10))=log_10(v)`

`u(1)=log_10(v)`

`log_10(v)=u`

Remember that the logarithmic function is the inverse of the exponential function. So when you see

`10^u=v` the logarithm is asking what number do i have to raise the base to to get the argument of the logarithmic function.... for example `log_10(100)=2` which is the inverse of
`10^2=100`