1) (log5(5-4x+x^2)) / log5X = 2
2) Выразите log25(27), если lg5=a, lg3=b
3) Сколько целых решений имеет неравенство: 1-5logx2 + 6log(^2)x2 < 0
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1) (log5(5-4x+x^2)) / log5X = 2
2) Выразите log25(27), если lg5=a, lg3=b
3) Сколько целых решений имеет неравенство: 1-5logx2 + 6log(^2)x2 < 0
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1) (log5(5-4x+x^2)) / log5X = 2;
log5( 5 - 4x + x^2 ) = 2 * log5( x ); log5(x) != 0;
log5( 5 - 4x + x^2 ) = log5( x^2 );
5 - 4x + x^2 = x^2;
5 - 4x = 0;
-4x = -5;
x = 5/4;
Проверка:
5 - 4x + x^2 = 5 - 4 * ( 5 / 4 ) + ( ( 5 / 4 ) ^ 2 ) = 5 - 5 + ( 5 / 4 )^2;
( log5( 5 / 4 )^2 ) / ( log5( 5/ 4 ) = ( 2 * log5( 5 / 4 ) ) / log5( 5 / 4 ) = 2.