## simplifying logs

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....

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 Blog Entries: 1 i don't get your question: $$\frac{\log_{5}}{2}=\log_{x}$$

 Quote by icystrike i don't get your question: $$\frac{\log_{5}}{2}=\log_{x}$$
thats the right equation, i was just wondering if anyone could help me solve for that 'x'?

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## simplifying logs

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

Blog Entries: 1
 Quote by shocklightnin thank you so much, you make understanding logs really easy! thanks.
Its my pleasure (=

 Recognitions: Gold Member Science Advisor Staff Emeritus 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 $$\frac{log_5(a)}{2}= log_x(a)$$ for some a, what is x?" Then icystrike is answering a completely different question: $$\frac{log(5)}{log(2)}= log(x)$$ which is, in a sense, the "reverse" of the original question! If my interpretion is correct, since $log_x(a)= log(a)/log(x)$ and $log_5(a)= log(a)/log(5)$, where "log" on the right of each equation can be to any base, it follows that $$\frac{log(a)}{log(5)}= 2\frac{log(a)}{log(x)}$$ Now the "log(a)" terms cancel out and we have $$\frac{1}{log(5)}= \frac{2}{log(x)}$$ That is the equation you want to solve.

Blog Entries: 1
 Quote by 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 $$\frac{log_5(a)}{2}= log_x(a)$$ for some a, what is x?" Then icystrike is answering a completely different question: $$\frac{log(5)}{log(2)}= log(x)$$ which is, in a sense, the "reverse" of the original question! If my interpretion is correct, since $log_x(a)= log(a)/log(x)$ and $log_5(a)= log(a)/log(5)$, where "log" on the right of each equation can be to any base, it follows that $$\frac{log(a)}{log(5)}= 2\frac{log(a)}{log(x)}$$ Now the "log(a)" terms cancel out and we have $$\frac{1}{log(5)}= \frac{2}{log(x)}$$ That is the equation you want to solve.
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 (=

$$\log_x 7 \times \log_7 5 = 2$$