Question

( frac{log ^{2} a}{log h log _{c}}+frac{log ^{2} b}{log a operatorname{lng} c}+frac{lg ^{2} c}{log a log _{b}}=3 )
( begin{aligned} Rightarrow & frac{log ^{3} a cdot log +log ^{3} b+log ^{3} c}{log a log b log c}=3 & Rightarrow log a b C=0 &=text { ) } a b c=1 end{aligned} )

# If log, a. log, a + log, b. log, b + log, c.log, C = 3 (where a, b, c are different positive real numbers + 1), then find the value of abc.

Solution