Evaluate $\log_{\sqrt{5}} 125\sqrt{5}$.

Input:$\log_{\sqrt{5}} 125\sqrt{5}$

Intepretation:

$1.\log_{\sqrt{5}} 125\sqrt{5}$ (Scientific Calculator 2.0)

We want to know how many powers of $\sqrt5$ equal to $125\sqrt5$

Looking at the numbers, we can know that the power is an integer, therefore:

$1.\sqrt5^2=5$ $,\space2.\sqrt5^3=5\sqrt5$

$3.\sqrt5^4=25$$,\space4.\sqrt5^5=25\sqrt5$

$5.\sqrt5^6=125$$,\space6.\sqrt5^7=125\sqrt5$

Answer $=7$

Intepretation No.2:
$2.\sqrt5\cdot125\sqrt5$ (Wolfram Computational Engine)

Cancel the two $\sqrt5$ ($\sqrt5^2=5$)

$=5\cdot125$

$=625$

Answer $=625$

Hi  Jeffes,

Thanks for answering this and other questions, it is appreciated.

I just wanted to point out that you are using QED incorrectly.

QED is used at the end of proofs, it means.. 'thus it has been demonstrated'.

Here you are simplifying an expression, you are not proving anything. So it is not appropriate to add QED at the end :)

Mmmmm....and all along I thought "Q.E.D."   referred to  "Quit Eating Dinner !!! "