SOLUTION: find the domain of the following equation and solve them log(9,x)+2log(3,x)=5

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Question 1149552: find the domain of the following equation and solve them
log(9,x)+2log(3,x)=5
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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The equation is


    log%289%2C%28x%29%29 + 2log%283%2C%28x%29%29 = 5


The domain is  x > 0.


Next,  log%289%2C%28x%29%29 = %281%2F2%29%2Alog%283%2C%28x%29%29.   Therefore, equation (1) takes the form


    %281%2F2%29%2Alog%283%2C%28x%29%29 + 2log%283%2C%28x%29%29 = 5

    %285%2F2%29%2Alog%283%2C%28x%29%29 = 5

    %281%2F2%29%2Alog%283%2C%28x%29%29 = 1

    log%283%2C%28x%29%29 = 2

    x = 3%5E2 = 9.       ANSWER

Solved.

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On logarithms,  their properties and solving logarithmic equations  see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Evaluate logarithms without using a calculator
    - Simplifying expressions with logarithms
    - Solving logarithmic equations
    - Proving equalities with logarithms
    - Using logarithms to solve real world problems
    - Solving problem on Newton Law of cooling
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.