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 $x \log a = y \log b = z \log c = \log m$.This implies $x = \frac{\log m}{\log a} = \log_a m$,$y = \log_b m$,and $z = \log_c m$.Since $x, y, z$ are in $G.P.$,we have $\frac{y}{x} = \frac{z}{y}$.Substituting the values,we get $\frac{\log_b m}{\log_a m} = \frac{\log_c m}{\log_b m}$.Using the change of base formula $\frac{\log_b m}{\log_a m} = \log_b a$,we get $\log_b a = \log_c b$.

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

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