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Expert: - 6/20/2009


Question
Hello, I was wondering if you would be able to help me out. You
see, I am going into high school and enjoy math very much. I
was wondering what you think I should study? I studied pre-
algebra, and am now studying Algebra. I would be interested in
going far on this someday. So do you think I should start with
Trigonometry or Calculus? Or should I wait?
Also, I was wondering if you would mind explaining to me how
to solve this problem..
5 (to the 2x+1 power) = 3 (to the 4x+1 power)
It was another question on here but I could not follow how they
solved it.
If you could please answer these questions for me, that would
be great. I would really appreciate any help that I can get.
Thank you,
Alex

Answer
I believe you should study hard at what interests you.
However, don't just study hard at math.  Be sure and study at another field, for all fields use some degree of math.  You might also take courses in chemistry, physics, computer science, biology, etc.

Now to answer the question about 5^(2x+1) = 3^(4x+1).

I'll start of by taking the natural log, ln(), of both sides
since when that is done, exponets can be brought out front as multiples.  What this gives is ln(5^(2x+1)) = ln(3^(4x+1)),
which leads to (2x+1)ln(5) = (4x+1)ln(3).

Now if we multiply out we get 2xln5 + ln5 = 4xln3 + ln3.

Moving the factors with l to the left side and the constants to the right side gives 2xln5 - 4xln3 = ln3 - ln5.

In the left side, x can be factored out, give
x(2ln5 - 4ln3) = ln3 - ln5.

We can then divide by what is multiplied be x, giving
x = (ln3 - ln5)/(2ln5 - 4ln3).

I get a value for x of a little bigger than 0.4,
so work it out to get the real value.

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