6 SOLVING EXPONENTIAL EQUATIONS WITH LIKE BASES WHAT

6 SOLVING EXPONENTIAL EQUATIONS WITH LIKE BASES

WHAT YOU SHOULD LEARN I can solve exponential equations with like bases. I can solve exponential equations when the bases can be made the same.

EXPONENTIAL EQUATIONS equations that contains exponential expressions To solve we will use the Property of Equality for Exponential Functions For b > 0 and b ≠ 1; if bx = by, then x = y If 2 powers with the same base are equal then their exponents are equal

SOLVE BY EQUATING EXPONENTS 23 x-3 = 29 3 x-3 = 9 3 x = 12 x=4 Since thy have the same bases we can set their exponents equal to each other and solve for x. Check 23(4)-3 = 29 212 - 3= 29 29 = 29

YOUR TURN! 22 x = 2 x 56 x-4 = 54 x+8 72 x-1 = 73 x+7

SOLUTIONS 22 x = 2 x-2 2 x = x-2 x = -2 56 x-4 = 54 x+8 6 x – 4 = 4 x + 8 2 x = 12 x=6 72 x-1 = 73 x+7 2 x – 1 = 3 x + 7 -x = 8 x= -8 Be sure to check your answers!!!!!

SOLVE BY EQUATING EXPONENTS 4 x = (½) x-3 22(x) = 2 -1(x-3) 22 x = 2 -x+3 2 x = -x+3 3 x = 3 x=1 Common Base = 2 Distribute! How can we make ½ a base of 2? Negative exponents!!! Check 41= (½)1 -3 4= (½)-2 4 = 22

YOUR TURN! 2 x-6 = (1/8)4 3 -x = (1/27)2 x+5 43 x = (1/16)1

SOLUTIONS 2 x-6 = (1/8)4 2 x-6 =(2)-3(4) x-6=-12 x = -6 Be sure to check your answers!!!!!

SOLUTIONS 3 -x = (1/27)2 x+5 3 -x = 3 -3(2 x + 5) -x = -6 x – 15 5 x = -15 x = -3 Be sure to check your answers!!!!!

SOLUTIONS 43 x = (1/16)1 43 x = (4)-2(1) 3 x = – 2 x = -2/3 Be sure to check your answers!!!!!

YOUR TURN!!! 9 x = 3 x+2 X=2

YOUR TURN!!! 3 x = (1/9)x-3 X=2

YOUR TURN!!! 9 x+4 = 274 x X = 4/5