Key Concepts

• Logarithms have properties similar to exponential properties because logarithms and exponents are of inverse forms to one another.
• Use the inverse nature and the definition of the logarithm to prove the properties of logarithms.
• Recall that exponents are added when like bases are multiplied as a reminder that the logarithm of a product is equivalent to a sum of logarithms to the same base.
• Recall that exponents are subtracted when like bases are divided as a reminder that the logarithm of a quotient is equivalent to a difference of logarithms to the same base.

Key Equations

• [latex]\log_bx=y \ \Leftrightarrow \ b^y=x[/latex]
• [latex]\log_b\left(MN\right)=\log_b\left(M\right) + \log_b\left(N\right)[/latex]
• [latex]\log_b\left(\dfrac{M}{N}\right)=\log_b\left(M\right) - \log_b\left(N\right)[/latex]

Glossary

one-to-one property of exponents

states that [latex]a^m=a^n \Leftrightarrow m=n[/latex]

one-to-one property of logarithms

states that [latex]\log_b\left(M\right)=\log_b\left(N\right) \Leftrightarrow M=N[/latex]