How to solve x <mrow class="MJX-TeXAtom-ORD"> log 3

Sage Garrison

Sage Garrison

Answered question

2022-06-02

How to solve x log 3 ( x ) 1 27
How to solve this? My problem is to solve:
x log 3 ( x 4 ) 1 27 .
The log base is 3

Answer & Explanation

Erik Rivera

Erik Rivera

Beginner2022-06-03Added 3 answers

Following the suggestions above, we take the log base 3 of both sides to get
( log 3 x ) ( log 3 x 4 ) 3, using the fact that f ( x ) = log 3 x is increasing. Substituting u = log 3 x gives u ( u 4 ) 3 so u 2 4 u + 3 0
Then ( u 3 ) ( u 1 ) 0, so either u 1 or u 3
If u 1, then log 3 x 1 so 0 < x 3
If u 3, then log 3 x 3 so x 27
Therefore the solution is given by ( 0 , 3 ] [ 27 , )

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