Help with logarithms plz...history, tables, uses, graphs and explaining formulas plz thanx?

The expression can be rewritten as: (log2)^3 + (log5)^3 + (log5)*(log2^3) =(log2)^3 + (log5)^3 + (log5)*3*(log2) Now, say a =log2 and be = log5 but a + be = log2 + log5 = log(2*5) = log(10) = 1 then it becomes a^3+b^3+3ab Since (a+b)^3 = a^3 + b^3 +3ab(a+b) So if we multiply 3ab by (a+b) then it will not make any difference in our case because a+b = 1 therefore, a^3 + b^3 + 3ab(a+b) = (a+b)^3 which is 1^3 = 1 Ans. Or you can go in the opposite way...Since we are getting cubic terms then (log2 + log5)^3 = (log2)^3 + (log5)^3 + 3(log2)(log5)(log2 + log5 ) =(log2)^3 + (log5)^3 + 3(log2)(log5)(log2*5 ) =(log2)^3 + (log5)^3 + 3(log2)(log5)(1 ) =(log2)^3 + (log5)^3 + (log2^3)(log5) =(log2)^3 + (log5)^3 + (log8)(log5) which is giving expression =>The given expression is equivalent to (log2 + log5)^3 =(log2*5)^3 =1 Ans.

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