1. Solving Exponential Equations

2. Exponential Equations
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

3. Solve by equating exponents
Since they have the same bases we can set their exponents equal to each other and solve for x.
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4. Your turn
2 2𝑥 = 2 𝑥 −2
5 6𝑥 −4 = 5 4𝑥+8
7 2𝑥 −1 = 7 3𝑥+7

5. Solve by equating exponents
Since they do NOT have the same bases…we have to rewrite so they have common bases.
Common base = 2
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6. Your turn
4 𝑥 −2 = 8 𝑥 −5
16 2𝑥 −1 = 64 3𝑥+8
25 2𝑥 = 125 𝑥+10

7. Solve by equating exponents
Common base = 2
How can we make ½ a base of 2?
Negative exponents!!!
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8. You Try
2 𝑥−6 =( 1 8 ) 4
4 3𝑥 =( ) 15
3 −𝑥 = ( 1 27 ) 2𝑥+5

9. Your turn!
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10. Your turn!
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11. Your turn!
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12. Solving Exponential Equations WS
Practice/H.W.
Solving Exponential Equations WS