If x, y, z are in G.P. and a^x = b^y = c^z,th | vedclass

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(B) Given that $x, y, z$ are in $G.P.$,we have $y^2 = xz$.Let $a^x = b^y = c^z = m$.Taking logarithm on both sides,we get $x \log a = y \log b = z \lo

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$\log_b a = \log_c b$

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(B) Given that $x, y, z$ are in $G.P.$,we have $y^2 = xz$.Let $a^x = b^y = c^z = m$.Taking logarithm on both sides,we get $x \log a = y \log b = z \log c = \log m$.Thus,$x = \frac{\log m}{\log a} = \log_a m$,$y = \log_b m$,and $z = \log_c m$.Since $x, y, z$ are in $G.P.$,the common ratio is constant,so $\frac{y}{x} = \frac{z}{y}$.Substituting the values of $x, y, z$ in terms of logarithms,we get $\frac{\log_b m}{\log_a m} = \frac{\log_c m}{\log_b m}$.Using the change of base formula $\log_k n = \frac{\ln n}{\ln k}$,we have $\frac{\ln m / \ln b}{\ln m / \ln a} = \frac{\ln m / \ln c}{\ln m / \ln b}$.This simplifies to $\frac{\ln a}{\ln b} = \frac{\ln b}{\ln c}$.Therefore,$\log_b a = \log_c b$.

If $x, y, z$ are in $G.P.$ and $a^x = b^y = c^z$,then

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