If log _{a} b=log _{b} c=log _{c} a,then: | vedclass

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(C) Let $\log _{a} b = \log _{b} c = \log _{c} a = k$.From the definition of logarithms,we have:$b = a^k$,$c = b^k$,and $a = c^k$.Substituting the val

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$a = b = c$

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(C) Let $\log _{a} b = \log _{b} c = \log _{c} a = k$.From the definition of logarithms,we have:$b = a^k$,$c = b^k$,and $a = c^k$.Substituting the values:$c = (a^k)^k = a^{k^2}$.Since $a = c^k$,we substitute $a$ into the equation:$c = (c^k)^{k^2} = c^{k^3}$.For $c > 0$ and $c 
eq 1$,this implies $k^3 = 1$,so $k = 1$.If $k = 1$,then $\log _{a} b = 1 \Rightarrow a = b$,$\log _{b} c = 1 \Rightarrow b = c$,and $\log _{c} a = 1 \Rightarrow c = a$.Therefore,$a = b = c$.

If $\log _{a} b=\log _{b} c=\log _{c} a$,then:

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