Question

Rewrite the form In exponential form:
Log100 = x

Answer 1

`10^x=100`

Explanation:

You know how subtraction is the opposite of addition and division is the opposite of multiplication? A logarithm is the opposite of an exponent. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.

We know that
`3^2=9`; as a logarithm, the exponent gets moved to its own side of the equation, and we write the equation like this:
`\log_3{9}=2`, which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."

One historical quirk: because we use the decimal system, it's assumed that an expression like
`\log1000` uses base 10, and you'd interpret it as "What power do I raise 10 to to get 1000?"

The expression
`\log100=x` means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is
`10^x=100`.

(If we wanted to, we could also solve this:
`10^2=100`, so
`\log100=2`)