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Mathematical Logarithm and Logarithm Operation
Solution: let 3 A = 4 B = 6 C = X, because a, b and c are all positive numbers, so X >;; 1

Therefore, a=log3(x) (note: log3(x) stands for the base 3 logarithm of x), b=log4(x) and c=log6(x).

According to the inference of logarithm base formula, logm(n)×logn(m)= 1 (Note: the logarithm of n with base m and the logarithm of m with base n are reciprocal).

So 1/a=logx(3), 1/b=logx(4), 1/c=logx(6).

therefore

left = 2/a+ 1/b = 2 logx(3)+logx(4)= logx(3 2×4)= logx(36)

right = 2/c = 2 logx(6)= logx(6 ^ 2)= logx(36)

Visible, left = right.

Therefore: 2/a+1/b = 2/c.