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avoavo
@avoavo
July 2022
1
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Помогите пожалуйста !!! Срочно !!!
Найдите наименьший корень уравнения :
lg x + lg (x^2) + lg (x^3) + ... + lg (x^19) = 380
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Verified answer
Lg (x^2) = 2*lg(x)
lg (x^3) = 3*lg(x)
... lg (x^19) = 19*lg(x)
lg(x) * (
1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+11
+12
+13
+14
+15
+16
+17
+18
+19
) = 380
lg(x) * (9*20+10) = 380
lg(x) = 380 / 190 = 2
x = 10^2 = 100
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Answers & Comments
Verified answer
Lg (x^2) = 2*lg(x)lg (x^3) = 3*lg(x)
... lg (x^19) = 19*lg(x)
lg(x) * (1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19) = 380
lg(x) * (9*20+10) = 380
lg(x) = 380 / 190 = 2
x = 10^2 = 100