LOGARITHMS B32

If log_x81 – log₂64 = -2; find x

solution

log_x81 – log₂64 = -2

log_x81 – log₂2⁶ = -2

log_x81 – 6log₂2 = -2

log_x81 – 6 x 1 = -2

log_x81 – 6 = -2

log_x81 = -2 + 6

log_x81 = 4

81 = x⁴

3⁴ = x⁴      Powers cancel out

x = 3

Hence x = 3.

TRY THIS..............

 If log_x81 – log₅625 = 0; find x