Simplification of logarithm in senior high school mathematics 33) simplification: (lg5) ^ 2 + (2 / 3) * LG8 + lg5 · LG20 + (LG2) ^ 2 Hope to have a general process ~ thank you! Hard~

Simplification of logarithm in senior high school mathematics 33) simplification: (lg5) ^ 2 + (2 / 3) * LG8 + lg5 · LG20 + (LG2) ^ 2 Hope to have a general process ~ thank you! Hard~

=(lg5)^2+lg5·lg20+(2/3)*lg2^3+(lg2)^2
=lg5·lg(5*20)+2lg2+(lg2)^2
=2lg5+2lg2+(lg2)^2
=2lg(2*5)+(lg2)^2
=2+(lg2)^2
Formula LGA + LGB = LG (AB)
nlga=lga^n

Urgent question! Senior high school mathematics problem, the number of good master please enter
lg4+lg5.lg20+(lg5)^2
lg25+lg2.lg50+(lg^2)2
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I need a detailed breakdown process, the answer is known
Thank you. The answers of the other two are also very good~

lg4+lg5.lg20+(lg5)^2
=lg2²+lg5×(lg2+lg10)+lg²5
=2lg2+lg5×lg2+lg5×lg10+lg²5
=2lg2+lg5×(lg2+lg5)+lg5×1
=2lg2+lg5×1+lg5
=2(lg2+lg5)
=2
lg25+lg2.lg50+(lg^2)2
=lg5²+lg2×(lg5+lg10)+lg²2
=2lg5+lg2×lg5+lg2×lg10+lg²2
=2lg5+lg2×(lg5+lg2)+lg2×1
=2lg5+lg2×1+lg2
=2(lg5+lg2)
=2

On the condition of exponent and logarithm
If a > 1, Let f (x) = a ^ x + x-4 and G (x) = log (a) x + x-4 be m and N, then what is the range of 1 / M + 1 / N?

A ^ x = 4-x, M is the abscissa of the intersection of y = a ^ X and y = 4-x, log (a) x = 4-x, n is the abscissa of the intersection of y = log (a) x and y = 4-x, y = a ^ X and y = log (a) X are inverse functions of each other. The symmetric intersection of y = x is (m, n) (n, m) on y = 4-x, M + n = 41 / M + 1 / N = (M + n) / (MN) = 4 / MNM + n > = 2 radical Mn, Mn = 1