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**bigmansouf** Question:Show that $\displaystyle log_{a}b=\frac{1}{log_{b}a} $,

a) using the result $\displaystyle log_{a}b \times log_{b}c = log_{a}c $ ]b) from first principles

**I was able to do part a; **

[tex] log_{a}b=\frac{log_{a}C}{log_{b}C}=\frac{log_{c}b} {log_{c}a}= \frac{log_{b}b}{log_{b}a}= \frac{1}{log_{b}a

**but part b is what i am struggling with.** For me first principles means $\displaystyle \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h} $

and i have tried and gone no way please help