LOGARITHMS B37

If log_x625 – log₂64 = -4; find x

solution

log_x625 – log₂64 = -2

log_x625 – log₂2⁶ = -2

log_x625 – 6log₂2 = -2

log_x625 – 6 x 1 = -2

log_x625 – 6 = -2

log_x625 = -2 + 6

log_x625 = 4

625 = x⁴

5⁴ = x⁴      Powers cancel out

x = 5

Hence x = 5.