Aim: How do we solve exponential equation?

Do Now: solve for x:

2. 2x = 8

3. 82 43 x

1. x3 = 8

HW: Worksheet

If au = av, then u = v

This says that if we have exponential functions in equations and we can write both sides of the equation using the same base, we know the exponents are equal.

343 22 x Now we use the property above. The bases are both 2 so the exponents must be equal.

343 x We did not cancel the 2’s, We just used the property and equated the exponents.

You could solve this for x now. 3

7x

Let’s try one more:8

14 x

The left hand side is 4 to the something, but the right hand side can’t be written as 4 to the something (using integer exponents)

We could however re-write both the left and right hand sides as 2 to the something.

32 22 x So now that each side is written

with the same base we know the exponents must be equal.

32 x2

3x

Solve for x:

Solve for x:x

x

184

1

xx 132 22Write both sides of

equation with base 2

Multiply the exponents,22 )1(32 xx

xx 332 22 Set the exponents equal to each other xx 332 Solve for x 3x

xx 4)25.0( 2 Solve for x:

Write .25 as a fraction that is equal to ¼

Rewrite the bases as base 4

Multiply the exponents

Set the exponents equal and solve for x 2x = 2,x = 1

xx 4)4( 21

xx 44 2

xx 2

xx

282

1Solve for x:

Solve for x: 2054 3

2

x

Be careful !

This equation is not an exponential equation. This is an equation with fractional exponential

Remember! To get rid of the fractional exponential, we just multiply the powers of both sides by the reciprocal.

8

125

3525 xx1.

527

13

x

132 39 xx

2.

3.

4. 1255 1 x

5.x

x

93

11

3

-2

1/7

4

–1

You try the following for credit

6. Solve for x:27

64

4

36

x

7. Solve for x: 521923 x

8. Solve for x:

343

149 4x

9.Solve for x: 42 3

2

x

3

-6