Logarithm Question log <mrow class="MJX-TeXAtom-ORD"> 3 </mrow> </msub

Marco Villanueva

Marco Villanueva

Answered question

2022-05-14

Logarithm Question log 3 9 x + log 3 x = 4
Edit: Mistake was at log 3 9 x 2 = 4 solution shown below
Confused on this question, not sure what I did wrong here.
log 3 9 x + log 3 x = 4
log 3 9 x + log 3 x = 4
log 3 9 x x = 4
log 3 9 x 2 = 4
2 log 3 9 x = 4 2
log 3 9 x = 2
3 2 = 9 x
9 = 9 x
x = 1

log 3 9 x 2 = 4
3 4 = 9 x 2
81 = 9 x 2 9
x 2 = 9
x = 3 , x 3

Answer & Explanation

HowOPpodopgtk3

HowOPpodopgtk3

Beginner2022-05-15Added 20 answers

The error is when you go from log 3 9 x 2 = 4 to log 3 9 x = 2. Since 9 x 2 = ( 3 x ) 2 , you should be writing log 3 3 x = 2 instead. Then proceed as before.
oglasnak9h01

oglasnak9h01

Beginner2022-05-16Added 2 answers

A slightly different approach
log 3 9 x + log 3 x = 4 log 3 9 + log 3 x + log 3 x = 4 2 + 2 log 3 x = 4
2 log 3 x = 2 log 3 x = 1 x = 3

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