4.5: Exponential and Logarithmic Equations

This section deals with solving equations with exponential and logarithmic functions.

Exponential Equations

Solving Exponential Equations
  1. Isolate the exponential expression.
    1. If there are two exponential expressions, put one on each side.
  2. Take the logarithm of each side. Bring down the exponent with Laws of Logarithms.
  3. Solve for the variable.
Solve $5^{2x} = 5^{x+1}$.
Solve $e^{3-2x} = 4$.

Logarithmic Equations

Solving Logarithmic Equations
  1. Isolate the logarithmic expression (combine with Laws of Logarithms if necessary).
    1. If there are two logarithmic expressions, put one on each side.
  2. Write the logarithm in exponential form, or exponentiate both sides with the base.
  3. Solve for the variable.
Solve $\log_2(25- x) = 3$.
Solve $\log(x^2 + 1) = \log(x - 2) + \log(x + 3)$.

Thanks for a good quarter! I wish you the best of luck studying and with your academic career :)