LOGARITHMS 20

If log_x3125 – log₃729 = -1; find x

solution

log_x3125 – log₃729 = -1

log_x3125 – log₃3⁶ = -1

log_x3125 – 6log₃3 = -1

log_x3125 – 6 x 1 = -1

log_x3125 – 6 = -1

log_x3125 = -1 + 6

log_x3125 = 5

3125 = x⁵

5⁵ = x⁵      Powers cancel out

x = 5

  

Hence x = 5.

TRY THIS………….

If log_k1024 – log₇343 = 7; find k