Question

If Log 20 = 1.301 what is the value of Logsub100 20?

I need the step by steps! I can’t find anything videos online to teach this to me

Answer 1

`log_(100)20 = 0.6505`

Explanation:

log20 = 1.301 (when you see only "log" with no base, it is taken as a base 10)

This basically means:

`10^(1.301) = 20` (This is the log in exponential form)

Since we don't know what
`log_(100)20` is equal to, we will say
`log_(100)20` = x

So to solve for
`log_(100)20` = x, you do the same thing. (convert to exponential form)

`100^(x) =20`

Now you will notice that both of these equations are equal to 20.

Since 20 = 20,

we can say
`100^(x)` =
`10^(1.301)`

Another way of saying 100, is
`10^(2)` (make the bases the same)

Now we get
`10^(2x) = 10^(1.301)`

(we get 2x because an exponent to the power of an exponent (
`2^(x)`) is the same as 2 * x)

Because you have the same base, you can just ignore the 10s and focus on the exponents. So you get:

2x = 1.301

x = 0.6505