I had never heard of a proof before coming to this forum (Schools FTW

).

And I though I would try some for fun.

The reason I am posting them here is because I believe they are not proofs, but rather a silly play in which nothing is proven.

(I considered putting this in the 'other' forum, but it contains mostly algebra. Sorry If I was wrong.)

Prove:

$\displaystyle log_bxy=log_bx+lob_by\,\,\,\because$

if

$\displaystyle log_bx=n$

$\displaystyle log_by=z$

then

$\displaystyle b^{z+n}=xy$

and

$\displaystyle z+n=log_bxy$

so

$\displaystyle

b^{log_bxy}=xy$

$\displaystyle xy=xy$

Prove:

$\displaystyle log_b\frac{x}{y}=log_bx-log_by\,\,\,\because$

say:

$\displaystyle log_bx=\gamma$

$\displaystyle log_by=\delta$

Then

$\displaystyle log_b\frac{x}{y}=\gamma-\delta$

so

$\displaystyle b^{\gamma-\delta}=\frac{x}{y}$

and

$\displaystyle {\gamma-\delta}=log_bx-log_by$

Prove:

$\displaystyle log_b(x^y)=ylog_bx\,\,\,\because$

$\displaystyle \frac{log_b(x^y)}{y}=log_bx$

$\displaystyle log_b(\sqrt[y]{x^y})=log_bx$

$\displaystyle log_bx=log_bx$

Are theses proofs? Or not?