SOLUTION: Hi, what is the log of log7 50= Sorry, I am not sure how to make the 7 a subscript. I understand I am trying to find the exponent of 7 that will produce 50. 7 squared is 49,

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Question 295955: Hi, what is the log of log7 50=
Sorry, I am not sure how to make the 7 a subscript.
I understand I am trying to find the exponent of 7 that will produce 50.
7 squared is 49, so what do I do from there?

Thanking You in Advance,
Jacinta

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
Your equation is:

This is true, if and only if

Take the log of both sides of this equation to get:

this log you are taking is to the base 10 which is the LOG function of your calculator.

Since, in general, , this equation becomes:

Divide both sides of this equation by to get:

*****

***** This equation is the log base conversion formula described below.

Use your calculator to get log of 50 divided by log of 10 to get:

which becomes:

That's your answer:

Plug into your original equation to get:

becomes:

this is true if and only if:

Use your calculator to determine that = 50, confirming that the answer of y = 2.010382138 is good.

You needed to know that, in general:

if and only if

There is also a log base conversion formula that will provide you with the same answer.

That conversion formula is:

y =

In your case, this conversion formula would work like this:

y =

If you look at what we did earlier, you will see that our solution yielded this exact formula.

That would be the equation denoted with ***** up above.

That equation was

Our conversion equation here is:

y =

y = is your original equation.

y = is the conversion equation.