Oblicz:
2log5(5)+3log2(4)=
4log2(jedna ósma)+log3(27)=
dla jednej wartości x log8(x^2-1)=2/3
2 log 5 [ 5 ] + 3 log 2 [ 4 ] = 2* 1 + 3*2 =2 + 6 = 8
4 log 2 [ 1/8 ] + log 3 [ 27 ] = 4* ( -3) + 3 = -12 + 3 = - 9
log 8 [ x^2 - 1 ] = 2/3
Założenie: x^2 - 1 > 0
log 8 [ x^2 - 1 ] = 2/3 <= > x^2 - 1 = 8 ^(2/3) <= > x^2 - 1 = [ 8^2]^)1/3) < =>
<=> x^2 - 1 = 64^ (1/3) <=> x^2 - 1 = 4 <=> x^2 = 5 < = > x = p(5)
p(5) - pierwiastek kwadratowy z 5
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2 log 5 [ 5 ] + 3 log 2 [ 4 ] = 2* 1 + 3*2 =2 + 6 = 8
4 log 2 [ 1/8 ] + log 3 [ 27 ] = 4* ( -3) + 3 = -12 + 3 = - 9
log 8 [ x^2 - 1 ] = 2/3
Założenie: x^2 - 1 > 0
log 8 [ x^2 - 1 ] = 2/3 <= > x^2 - 1 = 8 ^(2/3) <= > x^2 - 1 = [ 8^2]^)1/3) < =>
<=> x^2 - 1 = 64^ (1/3) <=> x^2 - 1 = 4 <=> x^2 = 5 < = > x = p(5)
p(5) - pierwiastek kwadratowy z 5