exponential equations

Bellwork: Get a sheet from the front desk and complete

Turn in the assignment from last class if you have not already

Exponential Equations

Recall: These are equations of the form y=abx-h+k, ones where the ‘x’ is in the exponent

x = the power you raise 2 to in order to get 8

x = the power you raise 2 to in order to get 4

x = the power you raise 2 to in order to get 5

y=2x

x = the power you raise 3 to in order to get 9

x = the power you raise 3 to in order to get 1

x = the power you raise 3 to in order to get 4

y=3x

Logarithms!

x = the power you raise 3 to in order to get 4

x = the power you raise 2 to in order to get 5

Let’s find some inverses

EX1:STEP 1: Replace f(x) with y.

STEP 2: Switch x and y.

STEP 3: Solve for y.

STEP 4: Replace y with f-1(x)

Let’s find some inverses

EX2:STEP 1: Replace f(x) with y.

STEP 2: Switch x and y.

STEP 3: Solve for y.

STEP 4: Replace y with f-1(x)

+1 +1

Let’s find some inverses

EX3:STEP 1: Replace f(x) with y.

STEP 2: Switch x and y.

STEP 3: Solve for y.

STEP 4: Replace y with f-1(x)

-3 -3

Let’s find some inverses

EX4:STEP 1: Replace f(x) with y.

STEP 2: Switch x and y.

STEP 3: Solve for y.

STEP 4: Replace y with f-1(x)

+4 +4

÷3÷3-1 -1

Intro to Logs: In Class Practice (Assignment)

Write the exponential function as a logarithm

Write the logarithm as an exponential function

Determine the inverse of the function

1) 2) 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)