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Logarithm cheat sheet (M J Rhoades)

Notes: When log b is written, it is for any log base even base "e"

When "ln" is written it means base "e" which is log base 2.718283

If just log is written, with no subscript, it implies base 10

When ln is written it means base "e"

Rules

Algebra

Log b (x) = N means b

N

= x

log b (0) is undefined

log b b = 1

log b 1 = 0

log b b

x

= x or ln (e

x

) = x

log

log

b

x

= x

log b (xy) = log b (x) + log b y and vice versa

log b (x

r

) = r log b x

log b

= log b (x) - log b (y) and vice versa

Inverse function of logs: example (x) = b

x

and g (x) = log b x

Inverse exponent functions of ln

(

-1

(x)) = e

ln (x)

= x

-1

( (x)) = ln (e

x

) = x

Special logs x = log e x and log x = log 10 x natural and common logs

Logarithm cheat sheet (M J Rhoades)

Notes: When log b is written, it is for any log base even base "e"

When "ln" is written it means base "e" which is log base 2.718283

If just log is written, with no subscript, it implies base 10

When ln is written it means base "e"

Rules

Algebra

Log b (x) = N means b

N

= x

log b (0) is undefined

log b b = 1

log b 1 = 0

log b b

x

= x or ln (e

x

) = x

log

log

b

x

= x

log b (xy) = log b (x) + log b y and vice versa

log b (x

r

) = r log b x

log b

= log b (x) - log b (y) and vice versa

Inverse function of logs: example (x) = b

x

and g (x) = log b x

Inverse exponent functions of ln

(

-1

(x)) = e

ln (x)

= x

-1

( (x)) = ln (e

x

) = x

Special logs x = log e x and log x = log 10 x natural and common logs