Solving logarithmic equation 2log(x)+1=log(19x+2)

Kayden Mills

Kayden Mills

Answered question

2022-11-04

Solving logarithmic equation 2 log ( x ) + 1 = log ( 19 x + 2 )
I know the solution has to be x = 2
However I can't find the manual steps (Wolfram doesn't know the manual steps either).
This is all I got
log ( x 2 ) + 1 = log ( 19 x + 2 )
log ( x 2 ) log ( 19 x + 2 ) = 1
log ( x 2 19 x + 2 ) = 1

Answer & Explanation

AtticaPlotowvi

AtticaPlotowvi

Beginner2022-11-05Added 18 answers

Hint: Write 1 as log 1 10 . Then take antilogs both sides.
Edit: The solution:
x 2 19 x + 2 = 1 10
Cross multiply:
10 x 2 = 19 x + 2
10 x 2 19 x 2 = 0
( x + 1 10 ) ( x 2 ) = 0
There you have it! x = 2. x = 1 10 gets rejected from your original question, but not from the one you solved. Think about it.

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