LOGARITHMS 12

If log_x625 – log₃729 = -4; find x

solution

log_x625 – log₃729 = -2

log_x625 – log₃3⁶ = -2

log_x625 – 6log₃3 = -2

log_x625 – 6 x 1 = -2

log_x625 – 6 = -2

log_x625 = -2 + 6

log_x625 = 4

625 = x⁴

5⁴ = x⁴      [Powers are alike. They cancel out]

x = 5

Hence x = 5.

TRY THIS………….

If log_m2048 – log₇343 = 8; find m