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The unknown b is stuck in the exponent position.
We can can fix that by using logarithms.
Log is the inverse operation of the exponential.
We'll take log of each side.
Log of what base tho?
Well, the base of our exponential is e,
so we'll take log base e of each side.
We'll apply one of our log rules next:
This allows us to take the exponent out of the log,
Another thing to remember about logs:
When the base of the log matches the inside of the log,
then the whole thing is simply 1,
So our equation simplifies to this,
As a final step, divide both sides by 3,
k, hope that helps!
So for this, you'll be using the pythagorean theorem, which is . In this case, 10 and 24 are the legs, and AB is the hypotenuse. Our equation will be
Firstly, solve the exponents:
Next, combine 100 and 576:
And lastly, square root both sides to get
And in short, Line AB is 26 ft, or the first option.