4 7 Green Solve Exponential and Logarithmic Equations

4. 7 (Green) Solve Exponential and Logarithmic Equations

Vocabulary: n Exponential equations are equations in which variable expressions occur as exponents. n Logarithmic equations are equations that involve logarithms of variable expressions.

Vocabulary: n Property of Equality for Exponential Equations: q n If b is a positive number other than 1, then bx = by if and only if x = y. Property of Equality for Logarithmic Equations: q If b, x, and y are positive numbers with b = 1, then logbx = logby if and only if x = y.

Solve by setting exponents = to each other n Solve 8 x = 4 x + 1 1. Turn equation into like bases 2. Power to a power means you multiply the exponents. 3. Set exponents = to each other since they have like bases. 4. Solve for x. 5. Check.

You Try: n Solve 53 x + 1 = 25 x + 1 x=1

Solve by taking the log of both sides n Solve 8 x = 23 1. Rewrite as a Log. 2. Use the change of base formula. Use calculator!!! 3. Check.

You Try: n Solve 43 x = 9 x≈0. 528

Solve using 2 Equivalent Logs n Solve log 8(x + 6) = log 8(4 – x) 1. Prop. Of Equality of Logs 2. Solve for x. 3. Check.

You Try: 1. Solve log 7(x + 2) = log 7(2 – 3 x) 2. ln(4 – 5 x) = ln(x + 10) n x=0 x=-1

Solve by creating Exponents on each side n Find the solution(s) of log x + log(x + 3) = 1 1. Use Properties of Logs to condense. or f k c e h c o t d e s e u n o u e s! Yo extran r e k a f. … s n o i t solu 2. Rewrite as an Exp. Equation. Solve for x. 3. Check.

You Try: 1. Solve log 6 x + log 6(x – 5) = 2 x=9 2. 2 ln x = ln(2 x – 3) + ln(x – 2) x=6 n