Logarithms Exponential Equations: Logarithmic Equations: Exponent Base Exponent What it equals

Let’s say I give you

I want you to find the inverse of this function

Logarithms

Logarithms

Exponential Equations:a

Logarithmic Equations:

log𝑏𝑎=𝑥Exponent

Base Base Exponent

What it equals

Reading Logarithms

▪ You read as: “the log of base b of a is x.

▪ Another way to say this is “the log is the exponents.”

▪ Just like in exponential equations, b > 0, b ≠ 1.

Example 1: Write the exponential equation in logarithmic form

26=64

You Try 1:Write the exponential equation in logarithmic form

45=1024

Example 2: Write the logarithmic equation in exponential form

log 5125=3

▪ A logarithm with base 10 is called a common logarithm. If no base is written for the logarithm, the base is assumed to be 10.

▪ Ex: log 4

▪ Special properties of logarithms:Logarithmic

FormExponential

FormExample

Logarithm of base b:

Logarithm of 1:

Evaluating Logarithms

▪ When it comes to evaluating logarithms, ask yourself this question, “what raised to the x power gives me this value?”

▪ Then decide what x is

Example 3: Evaluate

You Try 2: Evaluate

log 414

Example 4:Evaluate

log 10001000

Using Inverses

– m can be a numeric value or an expression

– m can be a numeric value or an expression

▪ When your bases aren’t the same, manipulate the base to help you.

Example 5: Simplify the expression

5 log5 𝑥

You Try 3: Simplify the expression

log 22𝑥

Example 6:

log 416𝑥

Graphing Logarithms

▪ Remember earlier in the lesson I told you logarithms were the inverse of exponentials.

▪ When it comes to graphing logarithms, make a table of the logarithm in exponential form and switch your x and y values.

▪ Furthermore everything vertical becomes horizontal and everything horizontal becomes vertical (this is in respects to your asymptotes).

Example 6: Find the inverse of the following and graph the inverse

x

-2

-1 2

0 4

1 10

2 28

x

2

4 0

10 1

28 2

Homework:

Page 277 17-30 all

(29-30 don’t describe the domain and range of each

function)