prove that $\displaystyle \log{b}x=\frac{\log{a}x}{\log{a}b}$. I'm having a little trouble getting started.
Follow Math Help Forum on Facebook and Google+
Originally Posted by VonNemo19 prove that $\displaystyle \log{b}x=\frac{\log{a}x}{\log{a}b}$. I'm having a little trouble getting started. $\displaystyle y = \log_b{x}$ $\displaystyle b^y = x$ $\displaystyle \log_a{b^y} = \log_a{x}$ $\displaystyle y\log_a{b} = \log_a{x}$ $\displaystyle y = \frac{\log_a{x}}{\log_a{b}}$
Hello, Another way : $\displaystyle \log_b x=\frac{\ln(x)}{\ln(b)}=\frac{\ln(x)}{{\color{red} \ln(a)}} \cdot \frac{{\color{red}\ln(a)}}{\ln(b)}=\log_ax\cdot\fr ac1{\log_ab}$
View Tag Cloud