LOGARITHM — Practice Questions (31 Problems)
31 multiple-choice questions on logarithms.
Try to solve each question independently before checking the answer key.
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Problem 1
Diketahui ${}^{p}\log 2 =8$ dan ${}^{q}\log 8 =4$. Jika $s=p^{4}$ dan $t=q^{2}$, maka nilai ${}^t\log s =\cdots$
Problem 2
Diketahui $a={}^{4}\log x$ dan $b={}^{2}\log x$. Jika ${}^{4}\log b+{}^{2}\log a=2$, maka $a+b$ adalah...
Problem 3
Jika ${}^{x}\log w=\dfrac{1}{2}$ dan ${}^{xy}\log w=\dfrac{2}{5}$ maka nilai ${}^{y}\log w$ adalah...
Problem 4
Diketahui bahwa:
${}^{3}\log x \cdot\ ^{6}\log x \cdot\ {}^{9}\log x =$ ${}^{3}\log x\cdot\ ^{6}\log x + {}^{3}\log x \cdot\ {}^{9}\log x+ ^{6}\log x \cdot\ {}^{9}\log x$
maka nilai $x$ yang memenuhi ada pernyataan...
(1) $\frac{1}{3}$ (2) $1$ (3) $4$ (4) $162$
Problem 5
Jika diketahui:
$f(n)={}^{2}\log 3 \cdot\ {}^{3}\log 4 \cdot\ {}^{4}\log 5 \cdots\ ^{n-1}\log n$ maka $f(8)+f(16)+f(32)+ \cdots +f(2^{30})=\cdots$
Problem 6
Sebuah lingkaran memiliki jari-jari $\log a^{2}$ dan keliling $\log b^{4}$, maka ${}^{a}\log b=\cdots$
Problem 7
Jika diketahui $x=\log a$, $y=\log b$ dan $z=\log c$. Maka bentuk sederhana dari $\log \left (\dfrac{a}{b^{2}}\sqrt{c} \right )$ dalam $x$, $y$ dan $z$ adalah...
Problem 8
$\dfrac{\left ({}^{5}\log 10 \right )^{2}-\left ({}^{5}\log 2 \right )^{2}}{{}^{5}\log \sqrt{20}}=\cdots$
Problem 9
Diketahui persamaan
${}^{2}\log {}^{3}\log \left({}^{5}\log a\right )={}^{3}\log {}^{5}\log \left({}^{2}\log b\right )={}^{5}\log {}^{2}\log \left({}^{3}\log c\right )=0$
maka nilai dari $a+b+c$ adalah...
Problem 10
Jika $(p,q)$ merupakan penyelesaian dari sistem berikut:
${}^{3}\log x\ +\ {}^{2}\log y =4$
${}^{3}\log x^{2}\ -\ {}^{4}\log 4y^{2} =1$
maka nilai $p-q=\cdots$
Problem 11
Nilai $\dfrac{{}^{2}\log 5 \cdot\ ^{6}\log 5+\ {}^{3}\log 5 \cdot\ ^{6}\log 5}{{}^{2}\log 5 \cdot {}^{3}\log 5}=\cdots$
Problem 12
Jika ${}^{2}\log (a-b)=4$, maka ${}^{4}\log \left (\dfrac{2}{\sqrt{a}+\sqrt{b}}+\dfrac{2}{\sqrt{a}-\sqrt{b}} \right )=\cdots$
Problem 13
${}^{3}\log x + 2\ {}^9 \log y = 3$ dan ${}^{3}\log \left( \dfrac{x-y}{2} \right) = 0 $, maka nilai $ x + y$ yang mungkin ada pada pernyataan...
(1) $2\sqrt{7}$ (2) $-4\sqrt{7}$ (3) $-2\sqrt{7}$ (4) $4\sqrt{7}$
Problem 14
Jika $x_{1}$ dan $x_{2}$ memenuhi $\left ( {}^{(2-x)}\log 27 \right )^{2}=9$ maka nilai $x_{1}+x_{2}$ adalah...
Problem 15
Jika $x_{1}$ dan $x_{2}$ memenuhi $\left ( {}^{3}\log (x+1) \right )^{2}=4$ maka nilai $x_{1} x_{2}$ adalah...
Problem 16
Jika $ ^{7}\log \left( {}^{3}\log \left( {}^{2}\log x \right ) \right ) =0$, nilai $2x+{}^{4}\log x^{2}$ adalah...
Problem 17
Jika diketahui $x$ dan $y$ adalah bilangan real dengan $x > 1$ dan $y > 0$. Jika $xy=x^{y}$ dan $\dfrac{x}{y}=x^{5y}$, maka $x^{2}+3y=\cdots$
Problem 18
Jika $4^{y+3x}=64$ dan ${}^{x}\log (x+12)-3{}^{x}\log 4=-1$ maka $x+2y=\cdots$
Problem 19
Jika $f \left(x^{2}+3x+1 \right) = {}^{2}\log \left(2x^{3}-x^{2}+7 \right)$, $x \geq 0$ maka $f(5)=\cdots$
Problem 20
Jika $a > 1$, $b > 1$ dan $c > 1$ maka $\left( {}^{a}\log \dfrac{1}{b} \right)\left( {}^{b}\log \dfrac{1}{c} \right)\left( {}^{c}\log \dfrac{1}{a} \right)=\cdots$
Problem 21
Jika ${}^{b}\log a=-2$ dan ${}^{3}\log b=\left( {}^{3}\log 2 \right)\left(1+ {}^{2}\log 4a \right)$, maka $4a+b=\cdots$
Problem 22
Jika diketahui ${}^{a}\log b + \left( {}^{a}\log b \right)^{2} + \left( {}^{a}\log b \right)^{3} + \cdots =2$, maka $ {}^{a}\log b + {}^{b}\log \sqrt[3]{a^{2}}=\cdots$
Problem 23
Jika $\log x=6$ dan $\log y=12$, maka nilai $\sqrt{\log \sqrt{x\sqrt{y\sqrt{x\sqrt{y\sqrt{x\sqrt{y\cdots}}}}}}}$ adalah...
Problem 24
Diketahui sistem persamaan
$\left\{\begin{matrix} 4^{x}+5^{y}=6 \\ 4^{\frac{x}{y}} = 5 \end{matrix}\right.$
Nilai $\dfrac{1}{x}+\dfrac{1}{y}=\cdots$
Problem 25
Jika $x_{1}$ dan $x_{2}$ memenuhi ${}^{4}\log x-{}^{x}\log 16= \dfrac{7}{6} - {}^{x}\log 8$, nilai $x_{1} \cdot x_{2}$ adalah...
Problem 26
Jika $2^{x}=2-\sqrt{3},$ maka $^{2+\sqrt{3}}\log 4^{x} =\cdots$
Problem 27
Jika ${}^{3x}\log \left( \dfrac{4-x^{2}}{x-3} \right)$ terdefenisi untuk $a < x < b$, maka $a+b=\cdots$
Problem 28
Jika untuk semua bilangan real $x < 7$ sehingga ${}^{x}\log \left( \dfrac{x^{2}+x-12}{x^{2}+x+12} \right)$ terdefenisi untuk $a < x < b$, maka $b-a=\cdots$
Problem 29
Bila $\log 2=p$, $\log 3=q$ dan $2^{x+1}=3^{2-3x}$, maka nilai $x+1$ adalah...
Problem 30
Jika $\left ( {}^{9}\log (x-1) \right )^{2}- {}^{9}\log (x-1)^{2}=a$ mempunyai tepat satu penyelesaian, yaitu $x=b$, maka $a+b=\cdots$
Problem 31
Jika $\left\{\begin{matrix} 2a+b =\ {}^{2}\log 45 \\ a+2b =\ {}^{2}\log 75 \end{matrix}\right.$ maka $a+b=\cdots$