Question 288335: express as a sum/difference log17 (x^3y^5/x^4)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! This expression looks like it is this:
If so, then the solution is as follows:
is the original equation.
Since, in general,  , then:
=  .
Since, in general,  , then:
=  , and then:
=  , and then:
=  .
Your answer should be that the original expression is equivalent to the final expression of:
To confirm, let x and y equal any value and solve both the final answer and the original expression to see if the answer comes out the same.
Let x = 3 and y = 5
Original expression of equals 27.53109739
Final expression of equals 27.53109739
Since the answers are the same (both = 27.53109739), the translation from the original expression to the final expression is good.
In order to confirm, use the log function of your calculator to calculate the results.
Once you have a term in the expression completed, then divide that result by the log of 17 to convert the log to the base of 10 answer into a log to the baseof 17 answer.
Example:
log(2,32) = 5 if and only if  = 32.
You can use your calculator to confirm that = 32.
You can then use the log function of your calculator to get the log of 32.
You will get 1.505149978.
You then divide that by the log of 2 to get 5.
Your answer is that:
= 32 if and only if  = 5
Your intermediate result, using the log function of the calculator, is that  = 1.5051499788.
Your final result, after dividing that by  is that = 5.
I will now repeat the calculations in more detail to show you how that works.
Your original expression is:
If we let x = 3 and y = 5, then this equation becomes:
Since, in general,  equals  , this expression becomes:
Simplifying by carrying out the indicated operations within the log function, this becomes:
 which becomes  .
Since, in general,  , and we want to convert from log base 17 to log base 10, then:
=  which equals 27.53109739.
Our first answer using the original expression is equal to 27.53109739.
We then go to the final expression and do the same thing.
The final expression is:
We let x = 3 and y = 5 to get:
We simplify this to get:
 .
We find  by using the log function of the calculator to get:
=  to get .387761935.
We plug that into our expression to get:
 .
We simplify this expression to get:
= 29.08214523 - 1.55104774 = 27.53109739.
Out second answer using the final expression is equal to 27.53109739.
Since both the original expression and the final expression got the same answer, the simplification of the original expression into the final expression is good.
Your answer is:
is equivalent to
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