Solving Exponential Equations

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Presentation transcript:

Solving Exponential Equations

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

Solve by equating exponents Since they have the same bases we can set their exponents equal to each other and solve for x. Check →

Your turn 2 2𝑥 = 2 𝑥 −2 5 6𝑥 −4 = 5 4𝑥+8 7 2𝑥 −1 = 7 3𝑥+7

Solve by equating exponents Since they do NOT have the same bases…we have to rewrite so they have common bases. Common base = 2 Distribute! Check →

Your turn 4 𝑥 −2 = 8 𝑥 −5 16 2𝑥 −1 = 64 3𝑥+8 25 2𝑥 = 125 𝑥+10

Solve by equating exponents Common base = 2 How can we make ½ a base of 2? Negative exponents!!! Distribute! Check →

You Try 2 𝑥−6 =( 1 8 ) 4 4 3𝑥 =( 1 16 ) 15 3 −𝑥 = ( 1 27 ) 2𝑥+5

Your turn! Be sure to check your answer!!!

Your turn! Be sure to check your answer!!!

Your turn! Be sure to check your answer!!!

Solving Exponential Equations WS Practice/H.W. Solving Exponential Equations WS