For $a,c0,\ a,c\ne1$ and $b0$: $\log_a b=\dfrac{\log_c b}{\log_c a}$ Examples \(\

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For $a,c>0,\ a,c\ne1$ and $b>0$: $\log_a b=\dfrac{\log_c b}{\log_c a}$ Examples $\begin{aligned} \log_9 x&=\dfrac{\log_3 x}{\log_3 9}=\dfrac{1}{2}\log_3 x\quad(x>0) \ \log_5 18&=\dfrac{\lg18}{\lg5}=\dfrac{\ln18}{\ln5}\approx1.80\quad(3\text{ s.f.}) \end{aligned}$ Reciprocal identity $\log_a b=\dfrac{1}{\log_b a}\quad(b\ne1)$ $\log_x3=$   $\quad(x>0,\ x\ne1)$

Accepted Answer

$\log_a b=\dfrac{\log_c b}{\log_c a}$

Change of Base and Its Proof

Change of Base and Its Proof

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