4.4 Solving Exponential and Logarithmic Equations

Solving Exponential Equations: If possible, express both sides as powers of the same base Equate the exponents Solve for variable

Solving Exponential Equations If it’s not possible to express both sides as powers of the same base: Isolate the exponential expression Take the log of both sides Use the rules for logs to “break down” the expressions Solve for the variable

Solving Exponential Equations Solve: Take the log of each side Use the rules for logs to “break down” the expression Solve for the variable (check your answer!) Any base can be used, and since you’ll want to use your calculator, that will probably be 10 x  0.675

Solving Logarithmic Equations: Use the rules for logs to simplify each side of the equation until it is a single log or a constant:

Solving Logarithmic Equations Log = Log Equate the arguments Solve the resulting equation Reject solutions that would mean taking the log of a negative number!

Solving Logarithmic Equations Log = Constant Turn logarithm into an exponential Solve and check