Asked by kayla
how do i solve this logarithm
log(base 9)X + 3log(base 3)X = 14
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.