What do these pairs have in common? sin and sin -1 + and - ÷ and cos and cos -1 tan and tan -1

HW Check

Inverses undo each other! So what undoes x when it’s an exponent? y = a∙b x Get me down!

Introducing… Logarithms! A logarithm is defined as follows: x is now safely on the ground!

Example 1: Write 25 = 5 x in logarithmic form.

Example 2: Write ⅛ = (½) x in logarithmic form.

Okay, we can get x down from the exponent, but what do we do with an expression like this? log = x Your calculator automatically uses log 10 when we press the LOG function the calculator. Try it! How does this help us?

Change of Base Formula What if we have an expression that doesn’t have a base of 10? log 9 81 = x Change of Base Formula log 9 81 = Change of Base Formula log 9 81 =

Example 3: Write 98 = 7 x in logarithmic form. Then solve

Example 4: Write 42 = 9 x+2 +7 in logarithmic form. Then solve.

Example 5: Write 56 = 5 x-9 – 4 in logarithmic form. Then solve.

So what undoes x when it’s an exponent? y = a∙b x Yesterday, we learned how to solve for a variable when it is an exponent. Get me down!

What do we do if we have a variable trapped in a log? So what undoes x when it’s an exponent? log 4 x = 78 Get me out of here!

Rewrite it as a exponential function! No longer trapped inside the log!

Example 1: Solve log 5 x = 2

Example 2: Solve 3log 8 x = 3

Example 3: Solve log 5 (x-2) = 8

Example 4: Solve log 5 (x-2)+4 = 3

Example 5: Solve 2log 5 (x+2) - 5= 3