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

x>5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x>13

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x>8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x<13

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Suggest Corrections

Similar questions

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

8 x^{2} - 13 x - 5

x^{2} - 3 x + 10

x, 6 x y, 5 + x, - 5 x^{2} y, 8, 15 a z^{2}, \frac{32 z}{x y}, \frac{y^{2}}{3 x}, \frac{13 x}{x}

Join BYJU'S Learning Program