Aku n MATEMATIKA cah SMA Nda: Logarithmic Inequalities

Senin, Oktober 31, 2011

Logarithmic Inequalities

Salam Sukses Mulia SELALU Untukmu

$inequality between logarithms of linear functions with equal bases$

$inequality between logarithms with bases, smaller that 1$

$inequality between logarithms with base 10$

$inequality between sum of logarithms and a number$

$inequality between difference of logarithms and a number$

$inequality between sum of logarithms with bases smaller than 1 and a number$

$inequality between logarithms with different bases$

$inequality between sum of logarithms with different bases and a third logarithm$

$inequality between difference of logarithms with different bases and a number$

$inequality between sum of logarithm with irrational number and logarithm with base the square of this irrational number$

$inequality between defference of logarithms with different bases and a number smaller than one$

$inequality between module of logarithm and a number$

$inequality between logarithm divided by another logarithm with the same bases and a number$

$inequality between logarithm of quadratic funciton divided by logarithm of linear function and a number$

$inequality between double logarithm and a number$

klik adja pada judul diatas n dapatkan solution dari tiap-tiap soal tersebut

Contoh soal
Tentukan HP dari :

$x\, ^{}{\, ^{2}log\, x+^{\, \frac{1}{4}}log\, 4}<4$
Jawab :
$^{\frac{1}{4}}log\, 4 =-1$
jadi soal sekarang

$x\, ^{}{\, ^{2}log\, x-1}<4$

kedua rua kita logarimakan dengan basis 2

${\color{Red} ^{2}log}\, x\, ^{}{\, ^{2}log\, x-1}<\: {\color{Red} ^{2}log}\,4$
$\left (^{2}log\, x-1 \right ). ^{2}log\, x<2$

misal : $^{2}log\, x=m$

$m^{2}-m-2<0\Rightarrow (m-2).(m+1)<0\Rightarrow HP.-1<m<2$
$-1<\, ^{2}log\, x<2$
$^{2}log\, \frac{1}{2}<\, ^{2}log\, x<\, ^{2}log\, 4$
$\frac{1}{2}<\, x<\, 4$
Syarat : x > 0 (numerus pada soal asal)
Jadi HP untuk soal diatas adalah irisan keduanya :