PROPERTIES OF LOGARITHMS

SOLVING LOGARITHMIC EQUATIONS

1. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.

Problem 2: Solve for x in the equation

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Answer: tex2html_wrap_inline41 is the exact answer and x=10.5427684616 is an approximate answer.

Solution:

Step 1: Since you cannot take the log of a negative number, we must restrict the domain (values of x) so that

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Step 2: Convert the original equation to an exponential equation with base e and exponent 3:

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Step 3: Add 1 to both sides of the above equation:

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Step 4: Divide both sides of the above equation by 2:

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is the exact answer and tex2html_wrap_inline53 is an approximate answer.

Check: Let's substitute the approximate value of the answer in the original equation and determine whether the left side of the equation equals the right side of the equation after the substitution. Remember we rounded the answer; therefore, the left and right sides of the equation will most likely be very close but may not equal

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Since the value of the left side of the equation is 3 when you substitute x = 10.5427684616, and the right side of the equal is 3, you have proved your answer.

If you would like to work on another problem, click on Problem.

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Author: Nancy Marcus

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