Using logarithms to solve the following equation to find x 9^(2x) = 27^(1-x) ?? I'm really struggling with this questions. I appreciate your help and if you can please show me your working out so I can understand it too

ajumbaretu

ajumbaretu

Answered question

2022-11-18

Using logarithms to solve the following equation to find x
9 2 x = 27 1 x ?? I'm really struggling with this questions. I appreciate your help and if you can please show me your working out so I can understand it too

Answer & Explanation

ontzeidena8a

ontzeidena8a

Beginner2022-11-19Added 17 answers

Assuming it is this
9 2 x = 27 1 x
then you can use
9 = 3 2 and 27 = 3 3
to get
( 3 2 ) 2 x = ( 3 3 ) 1 x 3 4 x = 3 3 ( 1 x )
you can solve without logs. i.e.
3 a = 3 b iff a = b
Alice Chen

Alice Chen

Beginner2022-11-20Added 6 answers

As m log ( a ) = log ( a m ) , where both logarithm remain defined.
Taking logarithm in both sides,
2 x log ( 9 ) = ( 1 x ) log ( 27 )
Now log ( 27 ) = log ( 3 3 ) = 3 log 3 and log ( 9 ) = log ( 3 2 ) = 2 log 3
and log 3 0 can be cancelled safely from both sides

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