Question

Logarithm qn. plz help​

Answer 1

$\frac{ log_{a}(m) }{ log_{ab}(m) } \\ \\ = \frac{ log_{m}(ab) }{ log_{m}(a) } \\ \\ = log_{a}(ab) \\ \\ = log_{ a }(a) + log_{a}(b) \\ \\ = 1 + log_{a}(b) \\ \\ formulae \\ \\ log_{x}(y) = \frac{1}{ log_{y}(x) } \\ \\ \frac{ log_{e}(x) }{ log_{e}(y) } = log_{y}(x) \\ \\ log(xy) = log(x) + log(y) \\ \\ log_{x}(x) = 1$

hope it helps.

Answer 2

$HEYA \: \\ \\ log_{a}(m) \div log_{ab}(m) = 1 + log_{a}(b) \\ \\ l.h.s \\ log_{a}(m) \div log_{ab}(m) \\ \\ log_{a}(m) \ \: \: \times \: \: \: log_{a}(ab) \\ - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: log_{a}(m) \\ becoz \: \: \: log_{x}(y) = log_{t}(y) \div log_{t}(x) \\ \\ = log_{a}(ab) \\ \\ = log_{a}(a) + log_{a}(b) \\ becoz \: \: log_(pq) = log(p) + log(q) \\ \\ = 1 + log_{a}(b) \\ becoz \: \: \: log_{x}(x) = 1 \\ \\ \\ therefore \: \: l.h.s = 1 + log_{a}(b)$