Logs

What is a logarithm?

• the inverse of an exponent

• which means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x

Logarithms are Exponents

• log is short for logarithm

• when you perform a log function on a number the result is an exponent

• a log has a base to it just like the base of an exponent

• performing a log function is the inverse of an exponential function

log₂8 = 3

• Can be rewritten exponentially as 2³ = 8

• Said as "log base 2 of 8 equals 3"

• Thinking to self: "2 to what exponent will get me 8"

Multiple Choice

Rewrite in exponential form:

log₂ 0.25 = -2

• -2² = 0.25

• -2^0.25 = 2

• 2^-2 = 0.25

• No correct answer

Logarithms

What are they and how do you work with them?

Two forms

1. exponential

2. logaerithmic

Multiple Choice

Rewrite in logarithmic form:

6² = 36

• log₆ 2 = 36

• log₆ 36 = 2

• ln 36 = 2

• 6³⁶ = 2

Base of a Log

• The base of a log is the same as the base of an exponential

• log₂ 8= y means the same as 2^y=8

• We would read the above as log base 2 of 8

• Notice that 2 to the 3rd power is 8, so y=3 in the above equations

• so log₂8=3

• log₅25 = 2 since 5²=25

Log form vs Exponential form

• Watching the gif....

• Notice how base 2 stays the base of the exponential equation

• Notice how the result of the log, the ? becomes the exponent

• Notice how the 64, which we are taking the log of, becomes the result of the exponential

Multiple Choice

Change the following exponential equation into a log equation:

$$2^5=32$$  

• $$\log_25=32$$  

• $$\log_{32}5=2$$  

• $$\log_232=5$$  

• I hate logs. Nobody likes them.