Solve log_3 x+log_4 x=4.

prkosnognm

prkosnognm

Answered question

2022-07-28

Solve log 3 x + log 4 x = 4. Please include theproperties used.

Answer & Explanation

Steppkelk

Steppkelk

Beginner2022-07-29Added 11 answers

Here are the steps I used to get an answer.
By converting both logs to the same base (e)
ln x ln 3 + ln x ln 4 = 4
ln 4 ln x + ln 3 ln x ln 3 ln 4 = 4
( ln 4 + ln 3 ) ln x = 4 ln 3 ln 4
x = e 4 ln 3 ln 4 ln 3 + ln 4
ganolrifv9

ganolrifv9

Beginner2022-07-30Added 4 answers

We do as following
log x log 3 + log x log 4 = 4, multiple by LCD: Log3log4
( log 4 ) ( log x ) + ( log 3 ) log x = 4 log 3 log 4
factoring out log x
log x ( log 4 + log 3 ) = 4 log 3 log 4
log x = 4 ( log 3 ) ( log 4 ) log 4 + log 3 = 4 ( log 3 ) ( 2 log 2 ) 2 log 2 + log 3
take base 10 if needed
x = 10 8 ( log 3 ) ( log 2 ) 2 log 2 + log 3

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