Exercise Zone : Logaritma [4]
Table of Contents
Berikut ini adalah kumpulan soal mengenai Logaritma. Jika ingin bertanya soal, silahkan gabung ke grup Telegram, Signal, Discord, atau WhatsApp.
Tipe:
No.
Jika diketahuiALTERNATIF PENYELESAIAN
\begin{aligned}
\log12&=\log(2^2\dot3)\\
&=\log2^2+\log3\\
&=2\log2+\log3\\
&=\boxed{\boxed{2p+q}}
\end{aligned}
Jadi, log 12 = 2p + q .
No.
Nilai dari 2log 8 adalah ....- 1
- 2
- 3
- 4
- 5
ALTERNATIF PENYELESAIAN
\begin{aligned}
{^2\negthinspace\log 8}&={^2\negthinspace\log 2^3}\\
&=\boxed{\boxed{3}}
\end{aligned}
Jadi, nilai dari 2log 8 adalah 3.
JAWAB: C
JAWAB: C
No.
Nilai dari 2log 64 − 3log 27 − 5log 625 adalah ....- −2
- −1
- 0
- 1
- 2
ALTERNATIF PENYELESAIAN
\begin{aligned}
{^2\negthinspace\log 64}-{^3\negthinspace\log 27}-{^5\negthinspace\log 625}&={^2\negthinspace\log 2^6}-{^3\negthinspace\log 3^3}-{^5\negthinspace\log 5^4}\\
&=6-3-4\\
&=\boxed{\boxed{-1}}
\end{aligned}
Jadi, nilai dari 2log 64 − 3log 27 − 5log 625 adalah −1.
JAWAB: B
JAWAB: B
No.
Jika diketahui log 2 = p dan log 3 = q, maka nilai dari log 36 adalah ....- 2(p + q)
- 2p + q
- p + 2q
- p + q
- 2pq
ALTERNATIF PENYELESAIAN
\begin{aligned}
\log36&=\log\left(4\cdot9\right)\\
&=\log4+\log9\\
&=\log2^2+\log3^2\\
&=2\log2+2\log3\\
&=2p+2q\\
&=\boxed{\boxed{2(p+q)}}
\end{aligned}
Jadi, nilai dari log 36 adalah 2(p + q).
JAWAB: A
JAWAB: A
No.
Nilai dari- −3
- −2
- 1
- 2
- 3
ALTERNATIF PENYELESAIAN
\begin{aligned}
{^2\negthinspace\log 3}\cdot{^3\negthinspace\log 5}\cdot{^5\negthinspace\log 6}\cdot{^6\negthinspace\log 8}&={^2\negthinspace\log 8}\\
&={^2\negthinspace\log 2^3}\\
&=\boxed{\boxed{3}}
\end{aligned}
Jadi, nilai dari 2log 3 ⋅ 3log 5 ⋅ 5log 6 ⋅6log 8 adalah 3.
JAWAB: E
JAWAB: E
No.
Jika- \(\dfrac{3b}2\)
- \(\dfrac{2b}3\)
- b
- \(\dfrac1{b}\)
- \(\dfrac{2}{3b}\)
ALTERNATIF PENYELESAIAN
\(\begin{aligned}
{^{36}\negmedspace\log 25}&={^{6^2}\negmedspace\log 5^2}\\
&=\dfrac22{^6\negmedspace\log 5}\\
&=\dfrac1{^5\negmedspace\log 6}\\
&=\boxed{\boxed{\dfrac1b}}
\end{aligned}\)
Jadi, \({^{36}\negmedspace\log 25}=\dfrac1b\).
JAWAB: D
JAWAB: D
No.
Jika- $\dfrac34$
- 7
- 8
- 12
- 16
ALTERNATIF PENYELESAIAN
\(\begin{aligned}
\log(2x+y)&=1\\
2x+y&=10
\end{aligned}\)
\(\begin{aligned} 2^y&=\dfrac{2^{2x}}4\\[4pt] 4&=\dfrac{2^{2x}}{2^y}\\[4pt] 2^2&=2^{2x-y}\\ 2&=2x-y\\ 2x-y&=2 \end{aligned}\)
\(\begin{aligned} 2^y&=\dfrac{2^{2x}}4\\[4pt] 4&=\dfrac{2^{2x}}{2^y}\\[4pt] 2^2&=2^{2x-y}\\ 2&=2x-y\\ 2x-y&=2 \end{aligned}\)
\(\begin{aligned}
2x+y&=10\\
2x-y&=2&\color{red}+\\\hline
4x&=12\\
x&=3\rightarrow y=4
\end{aligned}\)
xy = 3 ⋅ 4 = 12
xy = 3 ⋅ 4 = 12
Jadi, xy = 12.
JAWAB: D
JAWAB: D
No.
Jika- $\dfrac{3a}2$
- $\dfrac{2a}3$
- $-\dfrac{2a}3$
- $\dfrac2{3a}$
- $\dfrac3{2a}$
ALTERNATIF PENYELESAIAN
\begin{aligned}
^{27}\negmedspace\log4&={^{3^3}\negmedspace\log2^2}\\
&=\dfrac23\cdot{^3\negmedspace\log2}\\[4pt]
&=\dfrac2{3\cdot{^2\negmedspace\log3}}\\
&=\color{blue}\boxed{\boxed{\color{black}\dfrac2{3a}}}
\end{aligned}
Jadi, $^{27}\negmedspace\log4=\dfrac2{3a}$.
JAWAB: D
JAWAB: D
No.
JikaALTERNATIF PENYELESAIAN
\(\begin{aligned}
^2\negmedspace\log5&={^2\negmedspace\log3}\cdot{^3\negmedspace\log5}\\
&=ab
\end{aligned}\)
\(\begin{aligned} ^6\negmedspace\log15&=\dfrac{^2\negmedspace\log15}{^2\negmedspace\log6}\\[4pt] &=\dfrac{^2\negmedspace\log(3\cdot5)}{^2\negmedspace\log(3\cdot2)}\\[4pt] &=\dfrac{^2\negmedspace\log3+{^2\negmedspace\log5}}{^2\negmedspace\log3+{^2\negmedspace\log2}}\\ &=\color{blue}\boxed{\boxed{\color{black}\dfrac{a+ab}{a+1}}} \end{aligned}\)
\(\begin{aligned} ^6\negmedspace\log15&=\dfrac{^2\negmedspace\log15}{^2\negmedspace\log6}\\[4pt] &=\dfrac{^2\negmedspace\log(3\cdot5)}{^2\negmedspace\log(3\cdot2)}\\[4pt] &=\dfrac{^2\negmedspace\log3+{^2\negmedspace\log5}}{^2\negmedspace\log3+{^2\negmedspace\log2}}\\ &=\color{blue}\boxed{\boxed{\color{black}\dfrac{a+ab}{a+1}}} \end{aligned}\)
Jadi, $^6\negmedspace\log15=\dfrac{a+ab}{a+1}$.
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