How do you solve these exponential equations?
3+2(3^(2x+3))=57
e^(2x)-13e^(x)+42=0
1 Answer
Jan 6, 2017
I tried this:
Explanation:
1) let us manipulate our expression to isolate the exponential:
We see that
The exponentials will be equal if the exponents are the same, or:
2) let us use a trick and write instead of
That is a quadratic equation that we solve using the Quadratic Formula to get:
Giving:
BUT
We said previously that
So:
For
And so (using the definition of natural log):
For
And so (using the definition of natural log):
