geno3141

You are aking:  What is the diameter of planet X?

But, in the next line, you are saying:  The diameter of planet X is 5235.98.

So, the diameter of planet X is 5235.98.

Start with 312,

        then 314,

        then 321,

        then 324,

        then 341,

        then 342,

        then 412,

       then ...

I'm just taking a stab at this; so, if anyone else has a better answer ...

natural logs are logs to the base e where e ≈ 2.7182818285... {an irrational number).

ln(212) / ln(5) is the quotient of ln(212) divided by ln(5)

This number would be the solution to the equation:  5^x  =  212.

I would suggest using the calculator at this site to get a decimal approximation.

Brackets in an equation are handled as if they are parentheses. If you have parentheses inside of other parenthese, it is easier to read if a set of parentheses is replaced with a set of brackets.

Now, there are situations where brackets can have other meanings; for instance, if you are using matrices, brackets can represent matrices, but if you aren't using special functions, they just work like parentheses.

If you have the product of an odd number of negative numbers, the product will be negative.

If you have the product of an even number of negative numbers, the product will be positive.

Do you have an odd number or an even number of negative numbers?

y² = 1/49

y  = ±√(1/49)  =  ±√1 / √49  =   ±1/7

√11300 = √100·√113 = 10√113 

√113 can't be simplified because 113 is a prime number.

You can set up a proportion:  12" / 1'  =  (3/8)" / x

Cross multiply:  12 · x  =  1 · (3/8)

Therefore:            12x  =  3/8

Divide by 12:            x  =  (3/8) ÷ 12

To divide, multiply by the reciprocal:  

                               x  =  (3/8) · (1/12)

                               x  =  3 / 96  =  1/32' (note that this answer is in feet)

Yes, it is a linear equation. When graphed, it is a vertical line whose x-intercept is -5. It is not a function.