simplifying logs

shocklightnin

1. The problem statement, all variables and given/known data
How do i solve for the subscript in:
(log (sub5)) / 2 = log(sub x)


2. Relevant equations

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3. The attempt at a solution

the original question was:

(log(subx)7)(log(sub7)5)=2
solve for x.
however i dont get how to solve for a subscript....

icystrike

i don't get your question:

[tex]\frac{\log_{5}}{2}=\log_{x}[/tex]

shocklightnin

thats the right equation, i was just wondering if anyone could help me solve for that 'x'?

icystrike

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shocklightnin

thank you so much, you make understanding logs really easy! thanks.

icystrike

Its my pleasure (=

HallsofIvy

Warning, shocklightnin. Icystrike may have misunderstood your question and given a wrong answer!

I would interpret your question, since you specifically stated that "5" and "x" were "subscripts" (I would say "bases") as
"If
[tex]\frac{log_5(a)}{2}= log_x(a)[/tex]
for some a, what is x?"

Then icystrike is answering a completely different question:
[tex]\frac{log(5)}{log(2)}= log(x)[/tex]
which is, in a sense, the "reverse" of the original question!

If my interpretion is correct, since [itex]log_x(a)= log(a)/log(x)[/itex] and [itex]log_5(a)= log(a)/log(5)[/itex], where "log" on the right of each equation can be to any base, it follows that
[tex]\frac{log(a)}{log(5)}= 2\frac{log(a)}{log(x)}[/tex]
Now the "log(a)" terms cancel out and we have

[tex]\frac{1}{log(5)}= \frac{2}{log(x)}[/tex]

That is the equation you want to solve.

icystrike

there was a missing "a" to the equation , thus , i check with him if he was referring to the above equation that i mention. Hope he will reply (=

Borek

Which seems to be

[tex]\log_x 7 \times \log_7 5 = 2[/tex]

and as far as I can tell it was not yet mentioned...