SOLUTION: Solve the equation {{{2^(x^3)=3^(x^2)}}}

Question 143994: Solve the equation
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Take the log of both sides

Rewrite the expressions using the identity

Subtract from both sides

Factor out the GCF

or Set each individual factor equal to zero

Let's solve the first equation

Take the square root of both sides. So this is our first answer.

--------------

Now let's solve the second equation

Add to both sides

Divide both sides by to isolate x

Use the change of base formula to simplify. So this is our other answer.

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Answer:

So the solutions are
or

which approximate to

or
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