SOLUTION: Hello, Why does √(10e) equal to e^1.65 ? Thank you!

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Question 363038: Hello,
Why does √(10e) equal to e^1.65 ?
Thank you!
Found 2 solutions by Theo, Edwin McCravy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
I don't see that they are equal.

sqrt(10*e) = 5.213714442

e^1.65 = 5.206979827

Did I misunderstand the question, or the given equation?

I originally assumed they were equal and tried to solve with logarithms and came up with the fact that they were different.

I then went back to the original equations and solved them without logs using my calculator and came up with the same conclusion - they are not equal.

you are talking about the square root of (10 * e) = e raised to the power of 1.65, aren't you?

you are meaning that e is the scientific constant of 2.718281828.... ?


Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
It doesn't equal that exactly

sqrt%2810e%29+=+5.213714442 to 9 decimal places

whereas

e%5E1.65=5.206979827 to 9 decimal places

So they're only equal to each other approximately to 2 decimal places.

To find what power of e sqrt%2810e%29 actually is, we let
x be the answer and so

sqrt%2810e%29=+e%5Ex

Square both sides

%28sqrt%2810e%29%29%5E2=+%28e%5Ex%29%5E2

10e=+e%5E%282x%29

Divide both sides by e or e%5E1

%2810e%29%2Fe=e%5E%282x%29%2Fe%5E1

Cancel e's on the left and subtract exponents 
on the right
 
10=+e%5E%282x-1%29

Taking natural logs of both sides:

ln%2810%29+=+2x-1

ln%2810%29%2B1+=+2x

Divide both sides by 2

%28ln%2810%29%2B1%29%2F2+=+x

evaluate that with a calculator and get

sqrt%2810e%29 is equal to (((e^1.651292546}}}

to 9 decimal places, not just 2 decimal places like (((e^1.65}}}

but it's still not exactly equal, but only approximately equal.

Edwin