LOGARITHMS 9

If log_x3125 – log₃81 = 1; find x

solution

log_x3125 – log₃81 = 1

log_x3125 – log₃3⁴ = 1

log_x3125 – 4log₃3 = 1

log_x3125 – 4 x 1 = 1

log_x3125 – 4 = 1

log_x3125 = 1 + 4

log_x3125 = 5

3125 = x⁵

5⁵ = x⁵      Powers cancel out

x = 5

Hence x = 5.

TRY THIS………….

If log_a1024 – log₇343 = 7; find a