Question

If x=y then show that a^(x) = a^(y)

Answer 1

Answer:

xy=yx

logxy=logyx

ylogx=xlogy

Differentiating

dxdylogx+xy=logy+yxdxdy

dxdy(logx−yx)=logy−xy

dxdyy(ylogx−x)=xxlogy−y

dxdy=x(ylogx−x)y(xlogy−y)

Hence proved.

Answer 2

${a}^{x} = {a}^{y}$

cancel both sides 'a'

$x = y$

Hence , proved .