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Exponential & Logarithmic Equations Exponential Equations with Like Bases Exponential Equations with Different Bases Logarithmic Equations

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Exponential Equations with Like Bases zIn an Exponential Equation, the variable is in the exponent. There may be one exponential term or more than one, like… zIf you can isolate terms so that the equation can be written as two expressions with the same base, as in the equations above, then the solution is simple. or

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Exponential Equations with Like Bases zExample #1 - One exponential expression. 1. Isolate the exponential expression and rewrite the constant in terms of the same base. 2. Set the exponents equal to each other (drop the bases) and solve the resulting equation.

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Exponential Equations with Like Bases zExample #2 - Two exponential expressions. 1. Isolate the exponential expressions on either side of the =. We then rewrite the 2nd expression in terms of the same base as the first. 2. Set the exponents equal to each other (drop the bases) and solve the resulting equation.

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Exponential Equations with Different Bases zThe Exponential Equations below contain exponential expressions whose bases cannot be rewritten as the same rational number. zThe solutions are irrational numbers, we will need to use a log function to evaluate them. or

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Exponential Equations with Different Bases zExample #1 - One exponential expression. 1. Isolate the exponential expression. 3. Use the log rule that lets you rewrite the exponent as a multiplier. 2. Take the log (log or ln) of both sides of the equation.

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Exponential Equations with Different Bases zExample #1 - One exponential expression. 4. Isolate the variable.

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Exponential Equations with Different Bases zExample #2 - Two exponential expressions. 1. The exponential expressions are already isolated. 3. Use the log rule that lets you rewrite the exponent as a multiplier on each side.. 2. Take the log (log or ln) of both sides of the equation.

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Exponential Equations with Different Bases zExample #2 - Two exponential expressions. 4. To isolate the variable, we need to combine the x terms, then factor out the x and divide.

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Logarithmic Equations zIn a Logarithmic Equation, the variable can be inside the log function or inside the base of the log. There may be one log term or more than one. For example …

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Logarithmic Equations zExample 1 - Variable inside the log function. 1. Isolate the log expression. 2. Rewrite the log equation as an exponential equation and solve for x.

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Logarithmic Equations zExample 2 - Variable inside the log function, two log expressions. 1. To isolate the log expression, we 1st must use the log property to combine a difference of logs. 2. Rewrite the log equation as an exponential equation (here, the base ise). 3. To solve for x we must distribute the e and then collect the x terms together and factor out the x and divide.

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Logarithmic Equations zExample 3 - Variable inside the base of the log. 1. Rewrite the log equation as an exponential equation. 2. Solve the exponential equation.

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