Bantuin dong logaritma:(.... Question from @mevatri

October 2018 1 91 Report

Bantuin dong logaritma:(

MicoArrafi Akan saya jawab soal yang susah saja :)
Jadi, soal yang mudah bisa anda buat latihan dasar :)

Nomor 6

$$\begin{align} \frac{1}{^{25}\log100}+\log5+\frac{1}{^4\log10}&={^{100}}\log25+\log5+{^{10}}\log4\\&={^{10^2}}\log5^2+\log5+{^{10}}\log4\\&={^{10}}\log5+\log5+{^{10}}\log4\\&=\log5+\log5+\log4\\&=\log(5\times5\times4)\\&=\log100\\&=\boxed2\ \bold{(b.)} \end$

Nomor 7

$$\begin{align} \frac{\log x\sqrt x+\log\sqrt y+\log xy^2}{\log xy}&=\frac{\log(\ x\sqrt x\times\sqrt y\times xy^2\ )}{\log xy}\\&=\frac{\log x^{\frac{5}{2}}y^{\frac{5}{2}}}{\log xy}\\&=\frac{\frac{5}{2}\times\log xy}{\log xy}\\&=\boxed{\frac{5}{2}}\ \bold{(e.)} \end$

Nomor 8

$$\begin{align} ^a\log\sqrt[3]a\times{^a}\log a\sqrt a&={^a}\log a^{\frac{1}{3}}\times{^a}\log a^{\frac{3}{2}}\\&=\frac{1}{\not3}\times\frac{\not3}{2}\\&=\boxed{\frac{1}{2}}\ \bold{(a.)} \end$

Nomor 9

$$\begin{align} ^{a^2}\log\frac{1}{b}\times{^{\sqrt b}}\log c^2\times{^{\frac{1}{c}}}\log a&={^{a^2}}\log b^{-1}\times{^{b^{\frac{1}{2}}}}\log c^2\times{^{c^{-1}}}\log a\\&=\frac{-1}{\not2}\times\frac{\not2}{\frac{1}{2}}\times\frac{1}{-1}\times{^a}\log b\times{^b}\log c\times{^c}\log a\\&=2\times1\\&=\boxed2\ \bold{(c.)} \end$

Nomor 10

$$\begin{align} \frac{\left(\ {^2}\log12\ \right)^2-\left(\ {^2}\log3\ \right)^2}{^2\log\sqrt6}&=\frac{(\ {^2}\log12+{^2}\log3\ )(\ {^2}\log12-{^2}\log3\ )}{^2\log\sqrt6}\\&=\frac{^2\log(12\times3)\times{^2}\log(12:3)}{^2\log\sqrt6}\\&=\frac{^2\log36\times{^2}\log4}{^2\log\sqrt6}\\&=\frac{^2\log6^2\times2}{^2\log6^{\frac{1}{2}}}\\&=\frac{2\times{^2}\log6\times2}{\frac{1}{2}\times{^2}\log6}\\&=\frac{2\times2}{\frac{1}{2}}\\&=2^3\\&=\boxed8\ \bold{(d.)} \end$

2 votes Thanks 1

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