Question

What is the exponential form of `log_b 35=3`?

Answer 1

`b^3=35`

Explanation:

Lets start with some variables

If we have a relation between `a," "b," "c` such that
`color (blue)(a=b^c`

If we apply log both sides we get

`loga=logb^c`

Which turns out to be

`color (purple)(loga=clogb`

Npw divding both sides by `color (red)(logb`

We get

`color (green)(loga/logb=c* cancel(logb)/cancel(logb)`

[Note: if logb=0 (b=1) it would be incorrect to divide both sides by `logb`... so `log_1 alpha` isn't defined for `alpha!=1`]

Which gives us `color (grey)(log_b a=c`

Now comparing this general equation with the one given to us...
`color (indigo)(c=3`
`color (indigo)(a=35`

And so, we again get it in form
`a=b^c`

Here
`color (brown)(b^3=35`