SOLUTION: How to solve this question? : In each of the following, Express y in terms of x. (a) 3 log y = log 2 + log x

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Question 1154761: How to solve this question? :
In each of the following, Express y in terms of x.
(a) 3 log y = log 2 + log x
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Alog%28%28y%29%29=log%28%282x%29%29

log%28%28y%29%29=%281%2F3%29log%28%282x%29%29

.
(removed - not good path)
.

.

cross%28y=b%5E%28%281%2F3%29%28log%282x%29%29%29%29

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The solution and the answer by @josgarithmetic both are WRONG.

            The correct solution is below. 


We start from

    3*log(y) = log(2) + log(x).


As the post is written, the base of logarithms is 10; but it does not play any role in that what follows.


The domain of logarithm function is y > 0, x > 0.


From the given equation

    log%28%28y%5E3%29%29 = log(2x),

    y^3 = 2x

    y = root%283%2C2x%29.


ANSWER.  y = root%283%2C2x%29.

Solved.

For your safety, ignore the post by @josgarithmetic.

-------------------

On logarithms and their properties,  see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
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.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

How to solve this question? :
In each of the following, Express y in terms of x.
(a) 3 log y = log 2 + log x 
 

 ----- Multiplying each side by 1%2F3

matrix%281%2C3%2C+log+%28%28y%29%29%2C+%22=%22%2C+1%2F3%29+%2A+log+%28%282x%29%29 

matrix%281%2C3%2C+log+%28%28y%29%29%2C+%22=%22%2C+log+%28%282x%29%29%5E%281%2F3%29%29

Logs are EQUAL, so