If _ea, _eb, _ec are in an A.P.

Question

If ${\log }_{e}a,{\log }_{e}b,{\log }_{e}c$ are in an A.P. and ${\log }_{e}a-{\log }_{e}2b,{\log }_{e}2b-{\log }_{e}3c,{\log }_{e}3c-{\log }_{e}$ a are also in an A.P, then $a:b:c$ is equal to

Accepted Answer

${\log }_{e}a,{\log }_{e}b,{\log }_{e}c$ are in A.P.

$	herefore {b}^{2}=ac$ ..... (i)

Also

$\begin{gathered} {\log }_{e}(\frac{a}{2b}),{\log }_{e}(\frac{2b}{3c}),{\log }_{e}(\frac{3c}{a}) \ {(\frac{2b}{3c})}^{2}=\frac{a}{2b}	imes \frac{3c}{a} \ \frac{b}{c}=\frac{3}{2} \end{gathered}$

Putting in eq. (i) ${b}^{2}=a	imes \frac{2b}{3}$

$\begin{gathered} \frac{a}{b}=\frac{3}{2} \ a:b:c=9:6:4 \end{gathered}$

Solutions · 1