Diketahui $^5 \text{log 3} =a $ dan $^3 \text{log 2} = b$. Nilai $^6 \text{log 10}$ adalah ......
a.$\dfrac{a + b}{ab+1}$
b. $\dfrac{a + 1}{ab+1}$
c. $\dfrac{ab + 1}{ab+a}$
d. $\dfrac{ab + 1}{ab+b}$
e. $\dfrac{b + 1}{ab+1}$
Penyelesaian :
$\begin{align} ^6 \text{log 10} & = \dfrac{^3 \text{log 10}}{^3 \text{log 6}} \\ \\ & = \dfrac{^3 \text{log 2}\times 5}{^3 \text{log 2} \times 3} \\ \\ & = \dfrac{^3\text{log 2} +^3\text{log 5}}{^3\text{log 2} + ^3\text{log 3}} \\ \\ & = \dfrac{b + \frac{1}{^5 \text{log 3}}}{b + 1} \\ \\ & = \dfrac{b + \frac{1}{a}}{b + 1} \times \dfrac{a}{a}\\ \\ & = \dfrac {ab + 1}{ab + a} \end{align}$
JAWAB : C. $\dfrac {ab + 1}{ab + a}$
Diketahui $^3 \text{log 5} =a $ dan $^2 \text{log 3} = b$. Nilai $^6 \text{log 10}$ adalah ......
Penyelesaian :
$\begin{align} ^6 \text{log 10} & = \dfrac{^3 \text{log 10}}{^3 \text{log 6}} \\ \\ & = \dfrac{^3 \text{log 2}\times 5}{^3 \text{log 2} \times 3} \\ \\ & = \dfrac{^3\text{log 2} +^3\text{log 5}}{^3\text{log 2} + ^3\text{log 3}} \\ \\ & = \dfrac{\frac{1}{^2\text{log 3}} + a}{\frac{1}{^2\text{log 3}} + 1} \\ \\ & = \dfrac{\frac{1}{b} + a}{\frac{1}{b} + 1} \times \dfrac{b}{b}\\ \\ & = \dfrac {1 + ab}{1 + b} \, \text {atau }\\ \\ & = \bbox[5px,border:2px solid red]{ \dfrac {ab + 1}{b + 1} } \end{align}$
Diketahui $^2 \text{log 3} =a $ dan $^3 \text{log 5} = b$. Nilai $^6 \text{log 45}$ adalah ......
Penyelesaian :
$\begin{align} ^6 \text{log 45} & = \dfrac{^3 \text{log 45}}{^3 \text{log 6}} \\ \\ & = \dfrac{^3 \text{log 3}^2\times 5}{^3 \text{log 3} \times 2} \\ \\ & = \dfrac{2 \times \, ^3\text{log 3} +^3\text{log 5}}{^3\text{log 3} + ^3\text{log 2}} \\ \\ & = \dfrac{2 \times 1 + b}{1 + \frac{1}{^2\text{log 3}}} \\ \\ & = \dfrac{2 + b}{1 + \frac{1}{a}} \\ \\ & = \dfrac{2 + b}{1 + \frac{1}{a}} \times \dfrac{a}{a}\\ \\ & = \bbox[5px,border:2px solid red]{ \dfrac {2a + ab}{a + 1} } \end{align}$
Diketahui $^2 \text{log 7} =a $ dan $^2 \text{log 3} = b$. Nilai $^6 \text{log 14}$ adalah ......
Penyelesaian :
$\begin{align} ^6 \text{log 14} & = \dfrac{^2 \text{log 14}}{^2 \text{log 6}} \\ \\ & = \dfrac{^2 \text{log 2}\times 7}{^2 \text{log 2} \times 3} \\ \\ & = \dfrac{^2\text{log 2} + ^2\text{log 7}}{^2\text{log 2} + ^2\text{log 3}} \\ \\ & = \bbox[5px,border:2px solid red]{ \dfrac {1 + a}{1 + b} } \end{align}$
2 comments
Wynn Resorts Ltd. announces partnership with Wynn in Las
Wynn Resorts 의정부 출장샵 Ltd. today announced a partnership with Wynn Resorts 양주 출장샵 Ltd., a 오산 출장안마 Las Vegas casino and 김해 출장샵 hotel company. 성남 출장안마
Bonuses cheap jerseys,wholesale jerseys,wholesale jerseys,wholesale nfl jerseys,nfl jerseys,wholesale nfl jerseys from china,Cheap Jerseys china,Cheap Jerseys china,nfl jerseys,cheap jerseys you could try here
EmoticonEmoticon