Example:

log₂2^-13 = -13

Example:

e^{ln8 =} e^{log_e8 =} 8

Example:

log₃3² = 2

Product Property:

log_a(MN) = log_aM + log_aN

Example:

log₈(2*4) = log₈2 + log₈4

Quotient Property:

log_aM/N = log_aM - log_aN

Example:

log₈16/2 = log₈16 - log₈2

Power Property:

log_aM^r = r log_aM

Example:

log₂7³ = 3 log₂7

If log_aM = log_aN,

then M=N

Example:

If log₅(2x+3) = log₅3,

then 2x+3 = 3

If a^b = a^c,

then b = c

Example:

If 3^-x = 3^4,

then -x = 4

Logarithmic Expression:

y = log_ax

Example:

log₄16 = 2

Exponential Expression:

a^y = x

Example:

4² = 16

Common Log

log x = log₁₀x

Natural Log

ln x = log_ex

For domain in logarithmic function:

x > 0

Don't need to check domain if x is not on argument side.

Change of Base Theorem:

log_aM = (log_bM)/(log_ba)

Choose new base, 10 or e, because the calculator will do these.

Example:

log₅18 = (log₁₀18)/(log₁₀5) = (log18)/(log5)

Since Common Log says:

log₁₀x=logx