LOGARITHMS B36

If log_x49 – log₂128 = -5; find x

solution

log_x49 – log₂128 = -5

log_x49 – log₂2⁷ = -5

log_x49 – 7log₂2 = -5

log_x49 – 7 x 1 = -5

log_x49 – 7 = -5

log_x49 = -5 + 7

log_x49 = 2

49 = x²

7² = x²      Powers cancel out

x = 7

Hence x = 7.