Logarithms identities

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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 = 1

Logarithm of the product:

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

Logarithm of the division:

logarithm division formula 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 implied from logarithm features:

additional logarithm formula additional logarithm formula
log n alog m b = log m alog n b a log n b = b log n a

Logarithms comparison:

logarithms comparison formula