Solving Logs Subscript: (log(sub5))/2=log(subx)

• shocklightnin
In summary, the conversation is about solving for the subscript in the equation (log(sub x)7)(log(sub7)5)=2 by using the properties of logarithms. One person provides an equation and asks for help in solving for x, while another person answers a different question and provides a different equation. The correct equation to solve is \frac{1}{log(5)}= \frac{2}{log(x)}.
shocklightnin

Homework Statement

How do i solve for the subscript in:
(log (sub5)) / 2 = log(sub x)

--

The Attempt at a Solution

the original question was:

(log(subx)7)(log(sub7)5)=2
solve for x.
however i don't get how to solve for a subscript...

$$\frac{\log_{5}}{2}=\log_{x}$$

icystrike said:

$$\frac{\log_{5}}{2}=\log_{x}$$

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

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icystrike said:

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

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

Its my pleasure (=

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.

HallsofIvy said:
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 (=

shocklightnin said:
the original question was:

(log(subx)7)(log(sub7)5)=2

Which seems to be

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

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

What is a logarithm?

A logarithm is a mathematical function that calculates the power or exponent needed to produce a given number. It is the inverse of an exponential function.

What does the subscript in a log signify?

The subscript in a logarithm indicates the base of the logarithm. In the equation (log5), 5 is the base of the logarithm.

How do you solve for the value of x in (log5)/2=logx?

To solve for the value of x, we need to isolate it on one side of the equation. We can do this by multiplying both sides by 2, which gives us log5 = 2logx. Then, we can use the exponent rule of logarithms to rewrite the equation as logx2 = log5. Since the bases of the logarithms are the same, we can set the exponents equal to each other and solve for x. In this case, x = 5.

What is the significance of solving for x in this equation?

The equation (log5)/2=logx is useful in determining the value of x in exponential equations. It allows us to solve for x when the base of the logarithm is different from the base of the exponential function.

Can this equation be solved using a calculator?

Yes, this equation can be solved using a calculator by using logarithmic functions. Make sure to enter the base of the logarithm correctly and use the inverse function key to solve for x.

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