Question

If $lo{g}_{12}^{36}=\alpha$ then find value of $lo{g}_{24}^{48}$ in terms of $\alpha$

Answer 1

${\log }_{12}36=\alpha$

we have to find out

${\log }_{24}4l=\log 24(36+12)$

$2={\log }_{6\times 2}{6}^2$

$2=\frac{2\log 6}{\log 6+\log 2}\Rightarrow \log 6+\log 2=\frac{2\log 6}{\alpha }$

$=\frac{\log 8\times 6}{\log (6\times 4)}=\frac{\log 8+\log 6}{\log 6+2\log 2}$

$\frac{3\log 2+\log 6}{\log 6+2\log 2}$

$=\frac{\log 2}{\log 6+2\log 2}$

$=\frac{\log 2}{\log 6+2\log \left(2\right)}$

$=\frac{\log 2}{\frac{2\log 6}{\alpha }+\log 2}$

$=\frac{2\log 2}{2\log 6+2\log 2}=\frac{2\log 2}{\log \left({36.2}^{\alpha }\right)}$

$=2{\log }_{{36.2}^{\alpha }}2$