LOGARITHMS 22

If log_x 2401 – log₃729 = -4; find x

solution

log_x 2401 – log₃729 = -2

log_x 2401 – log₃3⁶ = -2

log_x 2401 – 6log₃3 = -2

log_x 2401 – 6 x 1 = -2

log_x 2401 – 6 = -2

log_x 2401 = -2 + 6

log_x 2401 = 4 

2401 = x⁴        2401=7x7x7x7=7⁴ by prime factors

7⁴ = x⁴      Powers cancel out

x = 7

Hence x = 7.

TRY THIS………….

If log_m2048 – log₆216 = 8; find m