Logarithms identities

Logarithm of b to base a is called the power which the a should be exponentiated to get the b:

c = log a bac = b , and b > 0, a > 0, a1

Basic features of the logarithms:

a log a b = b
log a 1 = 0
log a a = 1
log a an = n

Logarithm of the product:

log a (uv) = log a u + log a v

Logarithm of the division:

logarithm division formula

Logarithm of the powers and roots:

log a u n = nlog a u
logarithm power formula
logarithm power formula
logarithm root formula

Transfer to the new logarithm base formula:

new base logarithm transfer formula

Formulas, derived from logarithm features:

formula derived from the features of logarithm
formula derived from the features of logarithm
log n alog m b = log m alog n b
a log n b = b log n a

Logarithms comparison:

logarithms comparison formula

Other useful links:

Partial derivative step by step sample
Fraction decomposition step by step sample
Parametric derivative step by step sample

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