If-x-y-z-are-in-GP-and-a-x-b-y-c-z-then-

Question Number 26249 by Gabriel Wendell Celestino Roch last updated on 23/Dec/17

If x, y, z are in GP and a^{x} = b^{y} = c^{z}, then

Commented by Rasheed.Sindhi last updated on 23/Dec/17

y = rx, z = r^{2} x [r is common ratio]

a^{x} = b^{rx} = c^{r^{2} x}

x \log a = rx \log b = r^{2} x \log c

\log a = r \log b = r^{2} \log c

r = \frac{\log a}{\log b} = \frac{\log b}{\log c}

∴ \log a, \log b & \log c are also

in GP having ratio 1 / r resiprocal

to the ratio in GP x, y & z