Question

2log7(x+3)=log7(x^2+45)

Answer 1

2log7(x+3) = log7(x²+45)

2(x + 3) = log7(x² + 45)/log7

2(x +3) = (x² + 45)

2x + 3 = x² + 45

x² + 45 = 2x +3

x² -2x + 45 - 3 = 0

x² - 2x + 42 = 0

a = 1 , b = -2 , c = 42

▲ = b² - 4ac

▲ = 4 - 4(1)(42) = -164

x = -b±√▲/2a

√▲ = √-164 = √164i² =2i√41

x1 = (-(-2) + i√41) / 2*1 = 2 + 2i√41/2 = 1 + i√41

x1 = (-(-2) - i√41) / 2*1 = 2 - 2i√41/2 = 1 - i√41

S = {1 + i√41 ;  1 - i√41}

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18/02/2016 
Sepauto - SSRC
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