Asked by kayla

how do i solve this logarithm

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

Answers

Answered by Reiny
we need the same base in the logs

let log<sub>9</sub> x = y
then 9^y = x
3^2y = x
and log<sub>3</sub> x = 2y

so log<sub>9</sub> x = 2log<sub>3</sub> x

then
log(base 9)X + 3log(base 3)X = 14 becomes
2log<sub>3</sub> + 3log<sub>3</sub> - 14
5log<sub>3</sub> = 14
log<sub>3</sub> = 2.8
x = 3^2.8
= 21.674
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