Question

PROVE : log y base y = 1​

Answer 1

$\rm {a}^{b} = c \: can \: be \: written \: as :$

$\rm \: b = log_{a}(c)$

Now,

$\rm \: let \: \: log_{y}(y) = x \: \: ..........(i)$

Thus,

$\rm \: x = log_{y}(y) \: can \: be \: witten \: as :$

$\rm {y}^{x} = y$

$\rm = > \: {y}^{x} = {y}^{1}$

Equating exponents when base is same,

=> x = 1

$\rm \: log_{y}(y) = 1 \: \: ...........(from \: (i))$

Hence Proved!