Solving exponential equations Adapted from Walch Education

Laws of exponents Law General rule Specific example Multiplication of exponents b m • b n = b m + n 46 • 43 = 49 Power of exponents (b m) n = b mn (bc) n = b nc  n (4 6 ) 3 = 4 18 (4 • 2) 3 = 4 32  3 Division of exponents Exponents of zero b 0 = 1 40 = 1 Negative exponents and

Solving exponential equations Rewrite the bases as powers of a common base. Substitute the rewritten bases into the original equation. Simplify exponents. Solve for the variable.

Practice # 1 Solve 4x = 1024. Rewrite the base as powers of a common base. 41 = 4 44 = 256 42 = 16 45 = 1024 43 = 64 We now know that it is possible to write 1,024 as a power of 4

The solution to the equation 4x = 1024 is x = 5 Rewrite the equation so that both sides have a base of 4. 4x = 45 Now solve for x by setting the exponents equal to each other. x = 5 The solution to the equation 4x = 1024 is x = 5

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