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Mastering Exponential and Logarithmic Equation Solving

Learn how to efficiently solve exponential and logarithmic equations by expressing sides as powers of the same base, isolating expressions, using logarithmic rules, and simplifying step-by-step. Practice with various base options utilizing calculators.

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Mastering Exponential and Logarithmic Equation Solving

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  1. 4.4 Solving Exponential and Logarithmic Equations

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

  3. 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

  4. 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!) x 0.675 Any base can be used, and since you’ll want to use your calculator, that will probably be 10

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

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

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

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