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Solving a logarithmic equation PROBLEM TYPE 2

# Solving a logarithmic equation PROBLEM TYPE 2 - for...

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Solving a logarithmic equation: Problem type 2 Solve for : . (If there is more than one solution, write the solutions as a list.) We first rewrite so that one side of the equation has only logarithmic terms: . Next we use the rule for logarithm of a quotient to combine the logarithmic terms: . Writing the last equation in exponential form , we obtain . Using the method of cross products , we rewrite the previous equation and solve for . Therefore, is the solution of the equation . However, logarithms are defined

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Unformatted text preview: for positive inputs only, and is a solution of the original equation only if all logarithmic terms in this equation are defined. Checking the value of with and , we have the following: • , and . Because both logarithmic terms are undefined for , is not a solution of the original equation. Therefore, the answer is: For additional explanation, see your textbook: • Section 4.4: Exponential and Logarithmic Equations No solution ....
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