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The solution by @josgarithmetic is W R O N G.
Below find the correct solution.
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10x^2 - x - 2 = 9x^2
x^2 - x - 2 = 0
(x-2)*(x+1) = 0
The roots to the last equation are x= 2 and x= -1.
The value x= -1 does not work as the solution to the original equation,
since is not defined.
The value x= 2 is the solution: both the left side and the right side of the original equation are DEFINED at x= 2.
Answer. The given equation has one and only one solution x= 2.
Check. The left side is = = = .
The right side is the same value.
Solved.
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On logarithms and their properties, see the lessons
- WHAT IS the logarithm
- Properties of the logarithm
- Change of Base Formula for logarithms
- Solving logarithmic equations
- Using logarithms to solve real world problems
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Logarithms".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.