Explanation Given Information: The equation is log 2 ( x − 2 ) + log 2 x = 3 . Formula used: Product rule of logarithms: log a M + log a N = log a M N Calculation: Consider the equation. log 2 ( x − 2 ) + log 2 x = 3 Obtain the single logarithm using the product rule of logarithms. log 2 x ( x − 2 ) = 3 Express it in equivalent exponential equation. x ( x − 2 ) = 2 3 x ( x − 2 ) = 8 Apply the subtraction principle: Subtracting 8 from both the sides of the equation. x 2 − 2 x − 8 = 8 − 8 x 2 − 2 x − 8 = 0 Factorize the polynomial. ( x − 4 ) ( x + 2 ) = 0 Apply the principle of zero products. Either x + 8 = 0 x = − 8 Or, x + 2 = 0 x = − 2 Check for –-2. Substitute x = − 2 in log 2 ( x − 2 ) + log 2 x = 3 to check it satisfies the equation or not

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Chapter 12.6, Problem 65ES

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To calculate: The value of x by solving the logarithm log2(x−2)+log2x=3.

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Chapter 12.6, Problem 64ES

Chapter 12.6, Problem 66ES

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Chapter 12 Solutions

EBK ELEMENTARY AND INTERMEDIATE ALGEBRA

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The value of x by solving the logarithm log 2 ( x − 2 ) + log 2 x = 3 .

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