SOLUTION: Tell whether the x-value is a solution of the equation. ln x=9, x=e^9

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Question 418872: Tell whether the x-value is a solution of the equation.
ln x=9, x=e^9
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
ln(x) = 9
x+=+e%5E9 is a solution to this equation if, after substituting e%5E9 for x, the equation is a true statement. So we substitute:
ln%28e%5E9%29+=+9
and then figure out if this is true. If you understand logarithms well and know that the base of ln is e, then you already know the answer. If not, then...

Using a property of logarithms, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, we can move the exponent out in front:
9*ln(e) = 9
Since ln(e) = 1 by definition, this becomes:
9*1 = 9
or simply
9 = 9
This is a true statement so x+=+e%5E9 is a solution to your equation.