Another Logarithm Problem

N

Nazariy

Junior Member
Joined
Jan 21, 2014
Messages
124
I need some help on this.

I have tried a few things now, which don't work. i.e. converting base of a logarithm and then using substitution, completing square and arriving at nowhere.

Here is the system of equations:

xy = 64
(log y to base x) + (log x to base y) = 5/2
 
Nazariy said:
I need some help on this.

I have tried a few things now, which don't work. i.e. converting base of a logarithm and then using substitution, completing square and arriving at nowhere.

Here is the system of equations:

xy = 64
(log y to base x) + (log x to base y) = 5/2
Click to expand...
multiply both sides by (log x to base y). Then let u=(log x to base y)...
 
Nazariy said:
I need some help on this.

I have tried a few things now, which don't work. i.e. converting base of a logarithm and then using substitution, completing square and arriving at nowhere.

Here is the system of equations:

xy = 64
(log y to base x) + (log x to base y) = 5/2
Click to expand...

Can you find a relationship between logy(x) and logx(y)?

Start with:

Let logy(x) = a → ya = x

and

Let logx(y) = b → xb = y

and continue.....
 
Subhotosh Khan said:
Can you find a relationship between logy(x) and logx(y)?

Start with:

Let logy(x) = a → ya = x

and

Let logx(y) = b → xb = y

and continue.....
Click to expand...

Yeah, i know what is the relationship. So log y to base x is thus 1/log x to base y. I actually got to simplified quadratic form of the equation with logs (before posting question), it is just that I didn't continue after that(probably need a break for today). Thanks
 
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