LOGARITHMS F7

 If log_x 2401 – log₃729 = -2; find x

 

solution

 

log_x 2401 – log₃729 = -2

 

log_x 2401 – log₃3⁶ = -2

 

log_x 2401 – 6log₃3 = -2

 

log_x 2401 – 6 x 1 = -2

 

log_x 2401 – 6 = -2

 

log_x 2401 = -2 + 6

 

log_x 2401 = 4 

 

2401 = x⁴        2401=7x7x7x7=7⁴ by prime factors

 

7⁴ = x⁴      Powers cancel out

 

x = 7

 

Hence x = 7.