Solving Exponential Equations

Real World Use of Exponential Functions

• Population Growth• Money (Compound Interest)• Depreciation (Cars)• Half-Life (Radioactive Material)• Bacteria Growth

• One way to solve exponential equations is to use the property that if 2 powers w/ the same base are equal, then their exponents are equal.

• For b>0 & b≠1 if bx = by, then x=y

Exponential Equations

Solve by equating exponents

Check →

3 3 92 2x Since they have the same bases we can set their

exponents equal to each other and solve for x.

3 3 9x

4x 3 4 3 9

9 9

2 2

2 2

Your turn

Solve by equating exponents

3 14 8x x Since they do NOT have the same bases…we have to rewrite so they have common

bases.

Common base = 2

3 12 32 2x x6 3 32 2x x

6 3 3x x

1x Check →

3 1 1 14 8

64 64

Distribute!

Your turn

Solve by equating exponents3

14

2

xx

Common base = 2

32 12 2x x2 32 2x x

2 3x x

1x

Check →

1 31

2

2

14

2

14

2

4 2

4 4

How can we make ½ a base of 2?

Negative exponents!!!

Distribute!

You Try

Your turn!

Be sure to check your answer!!!

29 3x x

2x

Your turn!

Be sure to check your answer!!!

313 ( )

9x x

2x

Your turn!

Be sure to check your answer!!!

4 49 27x x

4

5x

H/W

p.488 #9,10,12,14,32,33