Fungsi Logaritma 1. 4(dalam bentuk pangkat)log (2x²+24) < 4(dalam bentuk pangkat)log (x²+10x) 2. 6(d.... Question from @Jeph

November 2019 1 30 Report

Fungsi Logaritma

1. 4(dalam bentuk pangkat)log (2x²+24) < 4(dalam bentuk pangkat)log (x²+10x)
2. 6(dalam bentuk pangkat)log (x²-16)-6(dalam bentuk pangkat)log (2x-7)> 2-6(dalam bentuk pangkat)log 9

MRizky099

1.)

$\displaystyle {}^no numeric noise key 1194\log(2x^2+24) < 1193\log(x^2+10x) \\ 2x^2+24 x^2+10x x^2-10x+24 0 (x-4)(x-6) 0\\$

• Pengubah nol

$\displaystyle (x-4)(x-6) = 0 \\ \beginno numeric noise key 1189no numeric noise key 1188 x-4 = 0 & atau x-6 =0 x = 4>• Uji titik<img src=$

• Syarat fungsi log

Syarat: $\log\big( f(x) \big) \to > 0 \\$ .

$>• Himpunan Penyelesaian Soal<img src=$

Jawaban:

$\displaystyle \bold{HP = \{x| 4 < x < 6, x \in R\}}$

2.)

$\displaystyle {}^no numeric noise key 1120\log(x^2-16)-{}^no numeric noise key 1119\log(2x-7) > 2-{}^no numeric noise key 1118\log(9) \\ 1117\log\left(\fracno numeric noise key 1116no numeric noise key 1115 \right) 1114\log\left(6^2 \right)-{}^no numeric noise key 1113\log\left(9 1112\log\left(\fracno numeric noise key 1111no numeric noise key 1110\right)>{}^no numeric noise key 1109\log\left(\fracno numeric noise key 1108no numeric noise key 1107\right) 1106\log\left(\fracno numeric noise key 1105no numeric noise key 1104\right) 1103\log(4) \fracno numeric noise key 1102no numeric noise key 1101 4 1100no numeric noise key 1099-4 0 1098no numeric noise key 1097 1096no numeric noise key 1095 1094no numeric noise key 1093 0\\$

• Pengubah nol pembilang

$\displaystyle x^2-8x+12 = 0 \\ (x-2)(x-6) = 0 \beginno numeric noise key 1089no numeric noise key 1088x-2 =0 & atau x-6 =0 x =2 6 \endno numeric noise key 1087\\$

• Pengubah dan syarat penyebut bukan nol

$\displaystyle 2x-7 \neq 0 \\ 2x 7 x \fracno numeric noise key 1084no numeric noise key 1083 \\$

• Uji titik

$\displaystyle \beginno numeric noise key 1070 \left\{ x < 2 \right\} &: 0 \to \frac{(0)^2-8(0)+12}no numeric noise key 1069 & =\frac{+}{-} \\ \fracno numeric noise key 1068no numeric noise key 1067 3 \frac{(3)^2-8(3)+12}no numeric noise key 1066 \frac{-}{-} > \left\{\fracno numeric noise key 1065no numeric noise key 1064 6 4 \frac{(4)^2-8(4)+12}no numeric noise key 1063 \frac{-}{+} 7 \frac{(7)^2-8(7)+12}no numeric noise key 1062 \frac{+}{+} \endno numeric noise key 1061 \therefore \boxedno numeric noise key 1060no numeric noise key 1059 \: \bigvee 6\right\} }\\$

• Syarat fungsi log

$\displaystyle \beginno numeric noise key 1048no numeric noise key 1047 \star \: {}^no numeric noise key 1046\log(x^2-16) & 1045\log(2x-7) \\ x^2-16 > 0 2x-7 (x+4)(x-4) 2x 7 x < -4 \vee 4 \fracno numeric noise key 1044no numeric noise key 1043 \therefore \boxedno numeric noise key 1042} 1041no numeric noise key 1040 \right\}}\endno numeric noise key 1039\\$

• Himpunan Penyelesaian soal

$\displaystyle \beginno numeric noise key 1029 hp &= HP_1 \bigcap hp_2 hp_3 \\ \left\no numeric noise key 1028no numeric noise key 1027 \bigcup x > 6\right\} 1026 1025no numeric noise key 1024 \right\}\\ \no numeric noise key 1023 \endno numeric noise key 1022\\ \therefore \boxedno numeric noise key 1021 }\\$