Logarithm Properties

When a logarithm has division inside of it, it expands using ________________.

• Addition
• Subtraction
• Multiplication
• Division

Rewrite log₃t = 5 in exponential form.

• 5^t=3
• log₃5 = log₃t
• t⁵=3
• 3⁵=t

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Write as a single log: log 12 + 2 log x

• log (12 + 2x)
• log (14x)
• log (12 * 2x)
• log (12x²)

Expand.

• 1/3 log x + log y + log z
• 1/3 log x + 1/3 log y + 1/3 log z
• 1/3 log x - 1/3 log y - 1/3 log z
• 3 log x + 3 log y + 3 log z

Expand.

• log x + 5 log y
• 5 log x + 5 log y
• 5 log x - log y
• log x - 5 log y

Condense to a single logarithm.

• ln x⁴/ y
• ln xy⁴
• ln x/ y⁴
• ln x⁴/ y⁴

Condense.

• log₂x²y¹⁰
• log₂x²+log₂y¹⁰
• log₂x²/y¹⁰
• log₂10xy

Condense

• log xyz³
• log (xy/z³)
• log x + log y + log z³
• log x³y³z³

Expand

• log₈ x + log₈ y + log₈ z
• 5log₈ x + 5log₈ y + 5log₈ z
• log₈ xy + 5log₈ z
• log₈ x + log₈ y + 5log₈ z