logarithms exponential equations: logarithmic equations: exponent base exponent what it equals
TRANSCRIPT
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)