Logarithms and their properties

Change all logarithms to the same base. Multiply the first two and cancel the intermediate logarithm. Finally account for the reversed base and argument.

For a valid shared base and positive arguments, logₐ m + logₐ n = logₐ(mn), logₐ m − logₐ n = logₐ(m/n), and k logₐ v = logₐ(vᵏ). A sum of logarithms is not the logarithm of the sum.

For a valid shared base and positive arguments, logₐ m + logₐ n = logₐ(mn), logₐ m − logₐ n = logₐ(m/n), and k logₐ v = logₐ(vᵏ). A sum of logarithms is not the logarithm of the sum.

Replace the logarithm of the quotient by a difference. Bring the exponents out as coefficients, then substitute the given values.

First use change of base to obtain ln c from the base-b logarithm and the known ln b. Then perform the requested addition or subtraction.

logₐ b = c means aᶜ = b. A logarithm is the exponent required on the base. Require a > 0, a ≠ 1 and b > 0. Thus a^(logₐ b) = b; the common logarithm has base 10.

logₐ b = c means aᶜ = b. A logarithm is the exponent required on the base. Require a > 0, a ≠ 1 and b > 0. Thus a^(logₐ b) = b; the common logarithm has base 10.

logₐ b = c means aᶜ = b. A logarithm is the exponent required on the base. Require a > 0, a ≠ 1 and b > 0. Thus a^(logₐ b) = b; the common logarithm has base 10.

logₐ b = c means aᶜ = b. A logarithm is the exponent required on the base. Require a > 0, a ≠ 1 and b > 0. Thus a^(logₐ b) = b; the common logarithm has base 10.

Write the root as a rational power. Apply the logarithm power rule and the value of ln e. A negative exponent does not make the argument negative.