Lesson 5.4: Logarithms and Properties

Lesson 5.4: Logarithms and Properties

An Introduction

Since

 $f\left(x\right)=10^x$  and  $f^{-1}\left(x\right)=\log x$  then  $10^{\log x}=x$  and  $\log10^x=x$ .

Similarly, since

 $f\left(x\right)=e^x$  and  $f^{-1}\left(x\right)=\ln x$  then  $e^{\ln x}=x$  and  $\ln e^x=x$ .

Multiple Choice

You know: $x^m\cdot x^n=x^{\left(m+n\right)}$ 

then

 $\log\left(mn\right)=$   

• log(m) + log(n)

• log(m) log(n)

• log(m+n)

Multiple Choice

You know: $\frac{x^m}{x^n}=x^{\left(m-n\right)}$ 

then

 $\log\left(\frac{m}{n}\right)=$   

• log(m) - log(n)

• log(m) / log(n)

• log(m-n)

It's important to remember that logs are inverses of exponents, so properties of logs relate to properties of exponents.

You can use this idea to help you remember important log properties

Go on to work on 5.4 & 5.5 today.

Use what we did here to reinforce the properties you learn.