Question

Find $x$ if ${\log }_2(x-5)>3$

• A. $x>15$
• B. $x>13$
• C. $x>18$
• D. $x<13$

Answer 1

The correct option is B

$x>13$

${\log }_2(x-5)>3$

By definition of logarithm

$x-5>0$

$\Rightarrow x>5$ ...................(1)

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

$(x-5)>2^3$

$\Rightarrow x>8+5$

$\Rightarrow x>13$ ................(2)

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