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6.5 Solving Exponential Equations Notes Exponential equations are equations in which ______________________________ occur as exponents. Property of Equality for Exponential Equations Words Two powers with the same positive base b, where b 1, equal if and only if their exponents are equal. Numbers If 2 x 25 , then x 5. If x 5, then 2 x 25. Algebra If b 0 and b 1, then b x b y if and only if x y. Solve the equation. Check your solution. 1. 34 x 312 2. 8x 5 820 3. 64 x 5 62 x 4. 56 x 3 5 3 4 x To solve some exponential equations, you must first rewrite each side of the equation using the same base. 5. 42 x11 1024 6. 83 2 x 512 7. 47 x 256 8. 49 x 2 343 190 Algebra 1 Student Journal 9. 366 x 1 65 x Copyright © Big Ideas Learning, LLC All rights reserved. 10. 9 x 4 813 x 11. 64 x 1 512 x 12. 62 x 362 x 1 *Sometimes, it is impossible to rewrite each side of an exponential equation using the same base. You can solve these types of equations by graphing each side and finding the points(s) of intersection. Exponential equations can have no solution, one solution, or more than one solution depending on the number of points of intersection. * Graphing Calculator* 13.You deposit $1000 in a savings account that earns 5% annual interest compounded yearly. a. Write an exponential equation to determine when the balance of the account will be $1500. b. Solve the equation. Homework #6: Chapter 6.5 Pg. 329 1,2, 3-11 odd, 19, 43, 50, 60-63 *YOU MUST HAVE COMPLETE SENTENCES FOR #1 Copyright © Big Ideas Learning, LLC All rights reserved. Algebra 1 Student Journal 191