The correct option is C x gt;13 log_2 (x 5) gt; 3 By definition of logarithm x 5 gt; 0 x gt; 5 —————(1) Since base of logarithm greater tha ...

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Logarithmic Inequalities

Find x if log...

Question

Find x if ${log}_{2} (x - 5) > 3$

x>5

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x>13

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x>8

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x<13

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Solution

The correct option is B
x>13

${log}_{2} (x - 5) > 3$

By definition of logarithm

x - 5 > 0

x > 5 ---------------(1)

Since base of logarithm greater than 1, then inequality is equivalent to

x - 5 > $2^{3}$

x > 8 + 5

x > 13 -------------(2)

The common part of equation 1 and equation 2 is x > 13

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