Question

how do i solve this logarithm

log(base 9)X + 3log(base 3)X = 14

Answer 1

we need the same base in the logs

let log₉ x = y
then 9^y = x
3^2y = x
and log₃ x = 2y

so log₉ x = 2log₃ x

then
log(base 9)X + 3log(base 3)X = 14 becomes
2log₃ + 3log₃ - 14
5log₃ = 14
log₃ = 2.8
x = 3^2.8
= 21.674