Trig Problem 2^x=3^(x^2-1)

I know how to solve this equation with algebra (using logarithms), but I've never seen this in the context of trigonometry. Could you kindly provide an example (perhaps copied from your text) of how you're supposed to use trig functions (sines, cosines, etc) to solve this?

Thank you.

Eliz.
 
I'm sorry I shouldn't have labeled this as a trig. problem. It's algebraic. I can use logarithims. Thanks.
 
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