## How to solve an equation with a variable as exponent?

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
mathpatient
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### How to solve an equation with a variable as exponent?

I'm asked to solve a problem with the equation 6^x = 24x^2

I thought it might begin thus:

6^x = (6)(4)x^2

6^x/6 = 4x^2

6^(x-1) = 4x^2

but I'm unsure if this is the correct technique or if another technique, (involving logarithms?) might be appropriate
I am not sure what to do about the right side of the equation. please help. thanks

postscript: answer given x = 3

maggiemagnet
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Joined: Mon Dec 08, 2008 12:32 am
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### Re: How to solve an equation with a variable as exponent?

I'm asked to solve a problem with the equation 6^x = 24x^2
I don't think there is any way to do this with algebra. The left side is an exponential and the right side is a polynomial. You can see the formal solution here:

http://www.wolframalpha.com/input/?i=so ... +%3D+24x^2

(Copy and paste the line above into your browser's location bar.)

One of the solutions is a whole number. I think you are probably supposed to do guess-and-check to find that one solution.