Exponential and Logarithmic Equations

Stacie Bender 9/21/14

One to One Properties                           Inverse Properties

a^x = a^y if and only if x = y

log_ax = log_ay if and only if x = y

If the bases are the same, the exponents are equal.

If you need to remove a log­_a, take a and raise it to both sides of the equation.

Solve

Round answers to three decimal places.

2(5^{x + 3}) = 128

2^{x + 1} = 16

e^2x + 2e^x – 8 = 0

ln x + ln (x + 2) = 5