SOLUTION: I am confused about how to solve this problem?? If loga=1/3logX-3logv, what is the value of a? I think I am to assume the base for a is 10? I am unclear as to what X and V ar

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am confused about how to solve this problem?? If loga=1/3logX-3logv, what is the value of a? I think I am to assume the base for a is 10? I am unclear as to what X and V ar      Log On


   

Question 1105687: I am confused about how to solve this problem??
If loga=1/3logX-3logv, what is the value of a?
I think I am to assume the base for a is 10? I am unclear as to what X and V are so that I can find the value of a? My daughter is doing online high school and I am trying to help her with her algebra II. The guide with her online school is not helpful.
Thank you!
Terri Dougan
Found 3 solutions by greenestamps, josgarithmetic, ikleyn:
Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


Thanks for taking the time to try to help your daughter....

x and v are variables; you won't get a numerical answer to the problem; you will get an answer involving x and v.

When a problem involving logarithms does not specify the base, it is assumed that the base is 10. However, in this problem we are working with variables instead of numbers; so the base is irrelevant -- the problem could be in any base.

A logarithm is an exponent, so the laws for dealing with logarithms are essentially the same as the laws for dealing with exponents. Specifically,

(1) log%28%28a%2Ab%29%29+=+log%28%28a%29%29%2Blog%28%28b%29%29
(2) log%28%28a%2Fb%29%29+=+log%28%28a%29%29-log%28%28b%29%29
(3) log%28%28a%5Eb%29%29+=+b%2Alog%28%28a%29%29

I believe the expression you are given is
%281%2F3%29log%28%28x%29%29+-+3log%28%28v%29%29

Using the basic laws of logarithms...
%281%2F3%29log%28%28x%29%29+=+log%28%28x%5E%281%2F3%29%29%29 [rule (3)]
3log%28%28v%29%29+=+log%28%28v%5E3%29%29 [rule (3)]

[rule (2)]
So a+=+x%5E%281%2F3%29%2Fv%5E3

Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Not completely clear and only one equation with three unknown variables.

I am assuming the equation is supposed to be this, but using only lower-case for the variables:
log%28%28a%29%29=%281%2F3%29log%28%28x%29%29-3%2Alog%28%28v%29%29

You cannot find any value for "a" because not enough information is given, unless you omitted it.

If you want base to be 10, then
log%28%28a%29%29=log%28%28x%5E%281%2F3%29%29%29-log%28%28v%5E3%29%29

log%28%28a%29%29=log%28%28%28x%5E%281%2F3%29%29%2F%28v%5E3%29%29%29


Result from that, equating what are in the logs should be a=x%5E%281%2F3%29%2Fv%5E3.



********************this part below looks like a mistake**********************
Also can be stated 10%5E%28%28x%5E%281%2F3%29%29%2F%28v%5E3%29%29=a----------and this is all that can be done. NO Value for a; just the expression. (Display might not work.)

If that is not displaying properly, that is is pure text,
a=10^((x^(1/3))/(v^3))

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
If loga = 1/3logX - 3logv, what is the value of a?
~~~~~~~~~~~~~~~~~~ 

If loga = 1/3logX - 3logv, then


log(a) = log%28%28root%283%2Cx%29%2Fv%5E3%29%29,


which implies


a = root%283%2Cx%29%2Fv%5E3.


Answer.  a = root%283%2Cx%29%2Fv%5E3.


On properties of logarithms, 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.


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The solution by  @josgarithmetic  is   W R O N G.