If a, b, c are in G.P.,then log_a x, log_b x, | vedclass

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(C) Given $a, b, c$ are in $G.P.$Since $a, b, c$ are in $G.P.$,we have $b^2 = ac$.Taking $\log$ on both sides,we get $2 \log b = \log a + \log c$.This

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$H.P.$

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(C) Given $a, b, c$ are in $G.P.$Since $a, b, c$ are in $G.P.$,we have $b^2 = ac$.Taking $\log$ on both sides,we get $2 \log b = \log a + \log c$.This implies that $\log a, \log b, \log c$ are in $A.P.$Therefore,$\frac{1}{\log a}, \frac{1}{\log b}, \frac{1}{\log c}$ are in $H.P.$Multiplying by $\log x$,we get $\frac{\log x}{\log a}, \frac{\log x}{\log b}, \frac{\log x}{\log c}$ are in $H.P.$Using the change of base formula $\log_a x = \frac{\log x}{\log a}$,we conclude that $\log_a x, \log_b x, \log_c x$ are in $H.P.$

If $a, b, c$ are in $G.P.$,then $\log_a x, \log_b x, \log_c x$ are in:

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