7.5 Laws of Logarithms

Front

Expand the logarithm: log₂(5x)

Back

log₂ 5 + log₂ x

Front

Expand: 6log₈ u - 2log₈ v

Back

6log₈ u - 2log₈ v

Front

Rewrite logₕ(xⁿ)

Back

nlogₕ x

Front

Simplify: 2log(x) + 3log(xy)

Back

log(x⁵y³)

Front

Condense: 3 log₂ x + 2 log₂ y - 4 log₂ z

Back

log₂(x³y²/z⁴)

Front

Definition: Product Rule of Logarithms

Back

logₐ(mn) = logₐ m + logₐ n

Front

Definition: Quotient Rule of Logarithms

Back

logₐ(m/n) = logₐ m - logₐ n

Front

Definition: Power Rule of Logarithms

Back

logₐ(mⁿ) = n * logₐ m

Front

Example of Product Rule: log₁₀(1000)

Back

log₁₀(10 * 100) = log₁₀ 10 + log₁₀ 100 = 1 + 2 = 3

Front

Example of Quotient Rule: log₁₀(100/10)

Back

log₁₀(100) - log₁₀(10) = 2 - 1 = 1