The idea

Logarithms

A logarithm is the inverse of an exponential — it answers "what power?". Why logs exist (naming the solution of equations like 2^x = 100), converting between log and index form, evaluating logs, the special values, and natural logs (ln).

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Pure · Exponentials & logarithms

Logarithms

Why it works

The question powers can't answer

You can already solve

x^2 = 100

: take the square root, and

x = 10

. Now try

2^x = 100.

The unknown has moved into the power, and nothing in your toolkit touches it there. You can trap it —

2^6 = 64

is too small,

2^7 = 128

is too big, so

x

is somewhere between

6

and

7

— but "somewhere between

6

and

7

" is not an answer.

A number with no name

Here is the trap you've set, drawn:

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