Question

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

• A. x>5
• B. x>13
• C. x>8
• D. x<13

Answer 1

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 $x>13$