6.05 Properties of logarithms

Adaptive

Worksheet

Interactive practice questions

Given that $a>1$a>1, fully simplify the expression $\log_a\left(a^9\right)$loga(a9).

Easy

< 1min

Given that $a>1$a>1, fully simplify the expression $\log_a\left(\sqrt{a}\right)$loga(√a).

Medium

< 1min

Given that $a>1$a>1, fully simplify the expression $\log_a\left(\frac{1}{a^2}\right)$loga(1a2).

Medium

< 1min

Given that $a>1$a>1, fully simplify the expression $\log_a\left(\frac{1}{\sqrt{a}}\right)$loga(1√a).

Medium

1min

Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents.

Given a numerical logarithmic expression, evaluate and generate equivalent numerical expressions using the properties of logarithms or exponents.

Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.