Lanjutan Contoh Soal Eksponen dan Logaritma (KTSP XII) Bagian 3

\begin{array}{ll}\\ \fbox{10}.&\textrm{Hitunglah}\\ &\begin{array}{ll}\\ \textrm{a}.\quad ^{10}\log 200+\: ^{10}\log 50&\textrm{f}.\quad ^{5}\log 250-\: ^{5}\log 6+\: ^{5}\log 12-\: ^{5}\log 20\\ \textrm{b}.\quad ^{3}\log 45-\: ^{3}\log 5&\textrm{g}.\quad ^{3}\log \sqrt{5}\times \: ^{4}\log \frac{1}{3}\times \: ^{5}\log 7\times \: ^{25}\log 49\\ \textrm{c}.\quad ^{\sqrt{6}}\log 12+\: ^{\sqrt{6}}\log 5-\: ^{\sqrt{6}}\log 10&\textrm{h}.\quad ^{b}\log \sqrt[5]{a^{2}}\times \: ^{a}\log b\\ \textrm{d}.\quad ^{\sqrt{5}}\log 4-\: ^{\sqrt{5}}\log 20+\: ^{\sqrt{5}}\log 125&\textrm{i}.\quad \displaystyle \frac{^{5}\log 8\times \: ^{49}\log 125\times \: ^{2}\log 6}{^{\sqrt{7}}\log 36}\\ \textrm{e}.\quad ^{25}\log 60-\: ^{25}\log 3-\: ^{25}\log 4&\textrm{j}.\quad \displaystyle \frac{^{\frac{1}{n}}\log m\times \: ^{q}\log p^{3}\times \: ^{t^{2}}\log r^{-2}}{^{t^{2}}\log p\times \: ^{n^{3}}\log r\times \: ^{q}\log m^{2}} \end{array} \end{array}.

Jawab:

\begin{array}{|l|l|}\hline \begin{aligned}\textrm{a}.\quad ^{10}\log 200+\: ^{10}\log 50&=\: ^{10}\log (200\times 50)\\ &=\: ^{10}\log 10000\\ &=\: ^{10}\log 10^{4}\\ &=4 \end{aligned}&\begin{aligned}\textrm{b}.\quad ^{3}\log 45-\: ^{3}\log 5&=\: ^{3}\log \displaystyle \frac{45}{5}\\ &=\: ^{3}\log 9\\ &=\: ^{3}\log 3^{2}\\ &=2 \end{aligned}\\\hline \begin{aligned}\textrm{c}.\quad ^{\sqrt{6}}\log 12+\: ^{\sqrt{6}}\log 5&-\: ^{\sqrt{6}}\log 10\\ &=\: ^{\sqrt{6}}\log \displaystyle \frac{12\times 5}{10}\\ &=\: ^{\sqrt{6}}\log 6\\ &=\: ^{\sqrt{6}}\log \left ( \sqrt{6} \right )^{2}\\ &=2 \end{aligned}&\begin{aligned}\textrm{d}.\quad ^{\sqrt{5}}\log 4-\: ^{\sqrt{5}}\log 20&+\: ^{\sqrt{5}}\log 125\\ &=\: ^{\sqrt{5}}\log \displaystyle \frac{4\times 125}{20}\\ &=\: ^{\sqrt{5}}\log 25\\ &=\: ^{\sqrt{5}}\log \left ( \sqrt{5} \right )^{4}\\ &=4 \end{aligned}\\\hline \begin{aligned}\textrm{e}.\quad ^{25}\log 60-\: ^{25}\log 3&-\: ^{25}\log 4\\ &=\: ^{25}\log \displaystyle \frac{60}{3\times 4}\\ &=\: ^{25}\log 5\\ &=\: ^{5^{2}}\log 5^{1}\\ &=\displaystyle \frac{1}{2} \end{aligned}&\begin{aligned}\textrm{f}.\quad ^{5}\log 250-\: ^{5}\log 6&+\: ^{5}\log 12-\: ^{5}\log 20\\ &=\: ^{5}\log \displaystyle \frac{250\times 12}{6\times 20}\\ &=\: ^{5}\log 25\\ &=\: ^{5}\log 5^{2}\\ &=2 \end{aligned}\\\hline \multicolumn{2}{|c|}{\textrm{Soal yang belum dibahas silahkan dikerjakan sebagai latihan}}\\\hline \end{array}.

\begin{array}{ll}\\ \fbox{11}.&\textrm{Hitunglah}\\ &\begin{array}{ll}\\ \textrm{a}.\quad \log \left ( ^{4}\log \left ( ^{2}\log 16 \right ) \right )&\textrm{f}.\quad \displaystyle \frac{\left ( ^{3}\log 36 \right )^{2}-\left ( ^{3}\log 4 \right )^{2}}{^{3}\log \sqrt{12}}\\ \textrm{b}.\quad ^{3}\log \left ( ^{3}\log \left ( ^{3}\log 27 \right ) \right )&\textrm{g}.\quad 16^{\: ^{^{2}}\log 3}+27^{\: ^{^{3}}\log \frac{1}{2}}-\displaystyle \frac{3^{\: ^{^{3}}\log 2}}{2^{\: ^{^{2}}\log 3}}\\ \textrm{c}.\quad ^{\frac{1}{2}}\log 3\times ^{9}\log 8&\textrm{h}.\quad 81^{\: ^{^{3}}\log 2}+16^{\: ^{^{2}}\log 3^{-\frac{1}{4}}}-\displaystyle \frac{5^{\: ^{^{25}}\log 16}}{9^{\: ^{^{3}}\log 2}}\\ \textrm{d}.\quad 9^{\: ^{^{9}}\log 4}+16^{\: ^{^{\frac{1}{2}}}\log 6}&\textrm{i}.\quad (\sqrt{3})^{\: ^{^{3}}\log 2}\times (6\sqrt{6})^{\: ^{^{6}}\log 4}-\displaystyle \left (\frac{1}{3}\sqrt{3} \right )^{\: ^{^{3}}\log 4}\\ \textrm{e}.\quad (\sqrt{8})^{\: ^{^{2}}\log 3}+5^{\: ^{^{5}}\log 16}& \end{array} \end{array}.

Jawab:

\begin{array}{|l|l|}\hline \begin{aligned}\textrm{a}.\quad &\log \left ( ^{4}\log \left ( ^{2}\log 16 \right ) \right )\\ &=\log \left ( ^{4}\log \left ( ^{2}\log 2^{4} \right ) \right )\\ &=\log \left ( ^{4}\log 4 \right )\\ &=\log 1=\: ^{10}\log 10^{0}\\ &=0 \end{aligned}&\begin{aligned}\textrm{b}.\quad &^{3}\log \left ( ^{3}\log \left ( ^{3}\log 27 \right ) \right )\\ &=\: ^{3}\log \left ( ^{3}\log \left ( ^{3}\log 3^{3} \right ) \right )\\ &=\: ^{3}\log \left ( ^{3}\log 3 \right )\\ &=\: ^{3}\log 1=\: ^{3}\log 3^{0}\\ &=0 \end{aligned}\\\hline \begin{aligned}\textrm{c}.\quad ^{^{\frac{1}{2}}}\log 3\times ^{9}\log 8&=\: ^{2^{-1}}\log 3^{1}\times \: ^{3^{2}}\log 2^{3}\\ &=\displaystyle \frac{1\times 3}{-1\times 2}\: \left (^{2}\log 3\times ^{3}\log 2 \right )\\ &=-\displaystyle \frac{3}{2} \end{aligned}&\begin{aligned}\textrm{d}.\quad 9^{\: ^{^{9}}\log 4}+16^{\: ^{^{\frac{1}{2}}}\log 6}&=9^{\: ^{^{9}}\log 4}+(2^{4})^{\: ^{^{2^{-1}}}\log 6}\\ &=4+2^{\: ^{^{2}}\log 6^{-4}} \\ &=4+\frac{1}{6^{4}}\\ &=4+\displaystyle \frac{1}{1296}=4\frac{1}{1296} \end{aligned}\\\hline \multicolumn{2}{|c|}{\textrm{Soal yang belum dibahas silahkan dikerjakan sebagai latihan}}\\\hline \end{array}.

Untuk jawaban e dan f ada silahkan ke sini

\begin{array}{ll}\\ \fbox{12}.&\textrm{Tentukanlah penyelesaian dari}\\ &\begin{array}{ll}\\ \textrm{a}.\quad ^{2}\log \left ( x^{2}-x-5 \right )=0&\textrm{i}.\quad ^{2}\log \left ( x^{2}-x-11 \right )=0\\ \textrm{b}.\quad ^{2}\log \left ( x^{2}-2x-7 \right )=0&\textrm{j}.\quad ^{2}\log \left ( x^{2}-2x-14 \right )=0\\ \textrm{c}.\quad ^{2}\log \left ( x^{2}-3x-9 \right )=0&\textrm{k}.\quad ^{2}\log \left ( x^{2}-3x-17 \right )=0\\ \textrm{d}.\quad ^{2}\log \left ( x^{2}-4x-11 \right )=0 &\textrm{l}.\quad ^{2}\log \left ( x^{2}-4x-20 \right )=0 \\ \textrm{e}.\quad ^{2}\log \left ( x^{2}-5x-13 \right )=0&\textrm{m}.\quad ^{2}\log \left ( x^{2}-5x-23 \right )=0\\ \textrm{f}.\quad ^{2}\log \left ( x^{2}-6x-15 \right )=0&\textrm{n}.\quad ^{2}\log \left ( x^{2}-6x-26 \right )=0\\ \textrm{g}.\quad ^{2}\log \left ( x^{2}-7x-17 \right )=0&\textrm{o}.\quad ^{2}\log \left ( x^{2}-7x-29 \right )=0\\ \textrm{h}.\quad ^{2}\log \left ( x^{2}-8x-19 \right )=0&\textrm{p}.\quad ^{2}\log \left ( x^{2}-8x-32 \right )=0 \end{array} \end{array}.

Jawab:

\begin{array}{|l|ll}\cline{1-1} \begin{aligned}\textrm{a}.\quad ^{2}\log \left ( x^{2}-x-5 \right )&=0\\ \left ( x^{2}-x-5 \right )&=1\\ x^{2}-x-6&=0\\ (x-3)(x+2)&=0\\ x=3\: \: \textrm{atau}\: \: x=-2& \end{aligned}&\Rightarrow &\begin{array}{|c|c|l|}\hline \multicolumn{3}{|c|}{\textrm{Numerus harus positif, yaitu}:\: \: x^{2}-x-5>0}\\ \multicolumn{3}{|c|}{.}\\\hline x&x^{2}-x-5&\textrm{Keterangan}\\\hline 3&(3)^{2}-(3)-5=1>0&\textrm{memenuhi}\\ -2&(-2)^{2}-(-2)-5=1>0&\textrm{memenuhi}\\\hline \end{array} \\\cline{1-1}\end{array}\\\\\\ \textbf{Catatan}:\\ \textrm{Untuk}\: \: ^{a}\log f(x)=0,\: \textrm{dengan}\: a>0,\: a\neq 1,\: \textrm{maka}\: f(x)=1..

\begin{array}{ll}\\ \fbox{13}.&\textrm{Tentukanlah penyelesaian dari}\\ &\begin{array}{ll}\\ \textrm{a}.\quad ^{7}\log (3x+1)=2&\textrm{f}.\quad ^{3}\log (x-3)=\: ^{9}\log 16\\ \textrm{b}.\quad ^{3}\log \left ( x^{2}-6x+2 \right )=2&\textrm{g}.\quad ^{2}\log \left ( 2x^{2}-4 \right )=\: ^{2}\log \frac{1}{4}\\ \textrm{c}.\quad ^{5}\log \left ( x^{2}-3x-7 \right )=1 &\textrm{h}.\quad \log (2x-3)-\log (x-3)=\log 5\\ \textrm{d}.\quad \log (x+1)+\log (x-3)=1 &\textrm{i}.\quad ^{5}\log x+\:^{5}\log (x+20)=\: ^{5}\log 125 \\ \textrm{e}.\quad ^{4}\log x+\: ^{4}\log (x-6)=2&\textrm{j}.\quad ^{5}\log (x+1)+\:^{5}\log (x-3)=1\\ \end{array} \end{array}.

Jawab:

\begin{array}{|l|ll}\cline{1-1} \begin{aligned}\textrm{b}.\quad ^{3}\log \left ( x^{2}-6x+2 \right )&=2\\ ^{3}\log \left ( x^{2}-6x+2 \right )&=\: ^{3}\log 3^{2}\\ x^{2}-6x+2&=9\\ x^{2}-6x-7&=0\\ (x-7)(x+1)&=0\\ x=7\: \: \textrm{atau}\: \: x=-1& \end{aligned}&\Rightarrow &\begin{array}{|c|c|l|}\hline \multicolumn{3}{|c|}{\textrm{Numerus harus positif, yaitu}:\: \: x^{2}-6x+2>0}\\ \multicolumn{3}{|c|}{.}\\\hline x&x^{2}-6x+2&\textrm{Keterangan}\\\hline 7&(7)^{2}-6(7)+2=9>0&\textrm{memenuhi}\\ -1&(-1)^{2}-6(-1)+2=9>0&\textrm{memenuhi}\\\hline \end{array} \\\cline{1-1}\end{array}\\\\\\ \textbf{Catatan}:\\ \begin{aligned}\textrm{Untuk}\: \: ^{a}\log f(x)=\: ^{a}\log p,\: \textrm{dengan}\: a>0,\: a\neq 1,\: f(x)>0,\: p>0,\: \textrm{maka}\: f(x)=p. \end{aligned}.

\begin{array}{ll}\\ \fbox{14}.&\textrm{Tentukanlah penyelesaian dari}\\ &\begin{array}{ll}\\ \textrm{a}.\quad ^{2}\log (3x-2)=\: ^{^{\frac{1}{2}}}\log \left ( x+1 \right )&\\ \textrm{b}.\quad ^{2}\log x+\: ^{2}\log \left ( x-1 \right )=\: ^{2}\log \left ( x+3 \right )&\\ \textrm{c}.\quad ^{2}\log x+\: ^{2}\log \left ( x^{2}-2x+1 \right )=\: ^{^{\frac{1}{2}}}\log \left ( x^{2}+2 \right ) &\\ \textrm{d}.\quad ^{3}\log (x^{2}-2x)-\: ^{3}\log (4x+1)=\: ^{3}\log 2x &\\ \textrm{e}.\quad ^{2}\log (x+3)-\: ^{2}\log (2x+1)=\: ^{4}\log (2x+1)-\: ^{4}\log (x+3)&\\ \end{array} \end{array}.

 

 

 

 

 

Tentang ahmadthohir1089

Nama saya Ahmad Thohir, asli orang Purwodadi lahir di Grobogan 02 Februari 1980. Pendidikan : Tingkat dasar lulus dari MI Nahdlatut Thullab di desa Manggarwetan,kecamatan Godong lulus tahun 1993. dan untuk tingkat menengah saya tempuh di MTs Nahdlatut Thullab Manggar Wetan lulus tahun 1996. Sedang untuk tingkat SMA saya menamatkannya di MA Futuhiyyah-2 Mranggen, Demak lulus tahun 1999. Setelah itu saya Kuliah di IKIP PGRI Semarang pada fakultas FPMIPA Pendidikan Matematika lulus tahun 2004. Pekerjaan : Sebagai guru (PNS DPK Kemenag) mapel matematika di MA Futuhiyah Jeketro, Gubug. Pengalaman mengajar : 1. GTT di MTs Miftahul Mubtadiin Tambakan Gubug tahun 2003 s/d 2005 2. GTT di SMK Negeri 3 Semarang 2005 s/d 2009 3. GT di MA Futuhiyah Jeketro Gubug sejak 1 September 2009
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