Section 4.5 Exp. & Log Equations

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Presentation transcript:

Section 4.5 Exp. & Log Equations Chapter 4 – Exponential and Logarithmic Functions Section 4.5 Exp. & Log Equations 4.5 - Exp. & Log Equations

Solving Exponential Equations Isolate the exponential expression on one side of the equation. Take the logarithm of each side, then use the Laws of Logarithms to “bring down the exponent.” Solve for the variable. 4.5 - Exp. & Log Equations

Examples – pg. 338 Find the solution of the exponential equation, rounded to four decimal places. 4.5 - Exp. & Log Equations

Solving Logarithmic Equations Type 1 Type 1 equations are when not all terms are logarithms. Steps: Isolate the logarithmic term on one side of the equation. Use the Laws of Logarithms to combine the logarithmic terms. Write the equation in exponential form (or raise the base to each side of the equation). Solve for the variable. Check your solutions in the ORIGINAL problem. 4.5 - Exp. & Log Equations

Examples Solve the logarithmic equations below. 4.5 - Exp. & Log Equations

Solving Logarithmic Equations Type 2 Type 2 equations are when all terms are logarithms. Steps: Use the Laws of Logarithms to combine the logarithmic terms. Set the argument on the left equal to the argument on the right. Solve for the variable. Check your solutions in the ORIGINAL problem. 4.5 - Exp. & Log Equations

Example Solve the logarithmic equation below. 4.5 - Exp. & Log Equations

Examples Solve the logarithmic (literal) equations below for the specified variable of y. 4.5 - Exp. & Log Equations

More Examples – pg. 338 Solve the logarithmic equation for x. 4.5 - Exp. & Log Equations