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log(10-3x) - 2log(x) = 0 ======>
log(10-3x) = 2log(x)
log(10-3x) = log(x^2)
10 - 3x = x^2
x^2 + 3x - 10 = 0
(x+5)*(x-2) = 0.
The roots are x= -5 and x= 2.
Of these two roots, only x= 2 is meaningful (since x= -5 does not survive under the logarithm).
ANSWER. x= 2.
CHECK. log(10-3x) - 2*log(x) = log(10-3*2) - 2*log(2) = log(4) - 2*log(2) = 2*log(2) - 2*log(2) = 0. ! Correct !
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
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.