Chapter 5: Q. 19 (page 351)

Solve the following equation for 'x'.
$\log_{2} (x - 4) + \log_{2} (x + 4) = 3$

Short Answer

Expert verified

The value of $x = 2 \sqrt{6}$

Step by step solution

Given Information

Determining the value of x in the equation:

$\log_{2} (x - 4) + \log_{2} (x + 4) = 3$

Calculation

Given

$\begin{array}{rcl} \log_{2} (x - 4) + \log_{2} (x + 4) & = & 3 \\ \log_{2} [(x - 4) (x + 4)] & = & 3 \\ \log_{2} (x^{2} - 16) & = & 3 \end{array}$

Taking anti-log on both sides

$\begin{array}{rcl} x^{2} - 16 & = & 2^{3} \\ x^{2} & = & 8 + 16 \\ x & = & \sqrt{24} or 2 \sqrt{6} \end{array}$

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Solve the following equation for 'x'.
$\log_{2} (x - 4) + \log_{2} (x + 4) = 3$

Short Answer

Step by step solution

Given Information

Calculation

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Solve the following equation for 'x'.log2x-4+log2x+4=3

Short Answer

Step by step solution

Given Information

Calculation

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Solve the following equation for 'x'.
$\log_{2} (x - 4) + \log_{2} (x + 4) = 3$