Question

What is the exponential form of the logarithmic equation?

Answer 1

`0.8^4=0.4096`

Explanation:

The introduction to logarithms and definition of it is explained in the first link.

0.8 is the base of both logarithm and exponent. Logarithm is the inverse function to exponent, so if 0.8 is together with 0.4096 on the same side of logarithm equation, it must be together with 4 in exponent equation.

Try to rotate other triplets of numbers in your head. For example
`2^3=8` (exponent)
`root(3)(8)=2` (root)
`log_2 8=3` (logarithm)

Exponentiation has this "third way" of expressing, because it's not commutative (like addition or multiplication)
`2*3=6` (multiplication)
`6-:3=2` (division)
`6-:2=3` (still division)

• colorful logarithms with khanacademy
• wiki about logarithms

Answer 2

`0.8^4=0.4096`.

Explanation:

In the logarithm,
`M=log_ab` is equivalent to
`a^M=b`.

For example, `log_10 1000` is the number that satisfies
`10^x=1000`. Since `10^3=1000`, `log_10 1000 =3`.

In this question, substitute `M=4, a=0.8` and `b=0.4096` to the formula above.