How to Solve Logarithmic Equations? Find x^2*y^5/z^4

[Mermaid4220]

Homework Statement

log base u (x)=2.26
log base u (y)=2.84
log base u (z)=4.38
find ;
x^2*y^5/z^4

Homework Equations

The Attempt at a Solution

I have tried many things raising each of the numbers to their exponents and dividing, using laws of the exponents it state we have to have the exact answer with no instructions as to what decimal point or just the formula or what...can anyone help either get me started or understand what I am supposed to do?

 

[verty]

I think what is meant is, be as exact as you can be and simplify that formula as much as possible. At the moment it has 3 unknowns, can you do something about that?

 

[Mermaid4220]

I inserted the numbers x=2.26 and so forth and tried many different ways and all the answers i got were not excepted...:( its probably an easy thing as it is in the first part of the homework but it seems I make the easiest thing hard for some reason :)

 

[CAF123]

I would first solve the equations for x,y and z separately. Then label 2.6, 2.84 and 4.38 by a,b,c (so that in the end you get an exponent u^f, where f is entirely in terms of a,b,c - this avoids mid calculation rounding errors) and substitute x,y,z into the expression you need to find the value of. I think this is what you were trying but couldn't get any further?

 

[LCKurtz]

Homework Statement

log base u (x)=2.26
log base u (y)=2.84
log base u (z)=4.38
find ;
x^2*y^5/z^4

Homework Equations

The Attempt at a Solution

I have tried many things raising each of the numbers to their exponents and dividing, using laws of the exponents it state we have to have the exact answer with no instructions as to what decimal point or just the formula or what...can anyone help either get me started or understand what I am supposed to do?

Call the quantity $w=\frac{x^2y^5}{z^4}$. What is $\log_u(w)$? Then what is $w$? The answer will depend on $u$.

 

[Mermaid4220]

Its actually called u= not w= does that make a difference?

 

[LCKurtz]

Its actually called u= not w= does that make a difference?

?

You are using u as the base of your logs aren't you? I was just giving a name to your expression.

 

[SammyS]

Homework Statement

log base u (x)=2.26
log base u (y)=2.84
log base u (z)=4.38
find ;
x^2*y^5/z^4

It's my experience that such a problem would likely to ask you
to find :

$\displaystyle \log_{\,u}\left( \frac{x^2y^5}{z^4}\right)\ .$​

Finding this quantity first would help, even if it's not asked for.

 

[Mermaid4220]

That is exactly what they want and I found the quantity and tried several different ways of doing it but the program Wiley will not accept the answers :( I will get help tomorrow at school thanks anyways guys :)