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SOLVING EXPONENTIAL EQUATIONS Two exponential expressions with the same base are equal when their exponents are equal. If am = an, then m = n, where a > 0, a 1, and m, n R. If two expressions are equal, then taking the logarithm of both expressions maintains their equality. If M = N, then logaM = logaN, where a > 0, a 1, and M, N > 0. Example Solve, rounding to 2 decimal places where necessary: a) 42x = 25–x b) 2x = 7 c) 3x+1 + 3x = 324 d) 2x+1 = 3x–1 Summary A To solve an exponential equation algebraically: write both sides of the equation with the same base set exponents equal to each other solve for the unknown OR B Example take the log of both sides of the equation using base 10 use the power rule for logs to simplify the equation solve for the unknown The half-life of radioactive radon is 4 days. Determine how long it will take 200g of radon to be reduced to 12.5g. t 1 h M(t) P 2 Homework: p.485–486 #1cdf, 2bcf, 3ace, 4a, 5, 7, 8ace, 10bc, 12, 14, 17ac