CONTOH SOAL LOGARITMA dan PEMBAHASANNYA

Contoh Soal Nomor 1

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. $\dfrac{b + 1}{ab+1}$

Pembahasan Contoh Soal Nomor 1

BUKA Hint

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. $\dfrac {ab + 1}{ab + a}$

Contoh Soal Nomor 2

Diketahui $^3 \text{log 5} =a $ dan $^2 \text{log 3} = b$. Nilai $^6 \text{log 10}$ adalah ......

Pembahasan Contoh Soal Nomor 2

BUKA Hint

Penyelesaian :

$\begin{align} ^6 \text{log 10} & = \dfrac{^3 \text{log 10}}{^3 \text{log 6}} \\ \\ & = \dfrac{^3 \text{log 2}\times 5}{^3 \text{log 2} \times 3} \\ \\ & = \dfrac{^3\text{log 2} +^3\text{log 5}}{^3\text{log 2} + ^3\text{log 3}} \\ \\ & = \dfrac{\frac{1}{^2\text{log 3}} + a}{\frac{1}{^2\text{log 3}} + 1} \\ \\ & = \dfrac{\frac{1}{b} + a}{\frac{1}{b} + 1} \times \dfrac{b}{b}\\ \\ & = \dfrac {1 + ab}{1 + b} \, \text {atau }\\ \\ & = \bbox[5px,border:2px solid red]{ \dfrac {ab + 1}{b + 1} } \end{align}$

Contoh Soal Nomor 3

Diketahui $^2 \text{log 3} =a $ dan $^3 \text{log 5} = b$. Nilai $^6 \text{log 45}$ adalah ......

Pembahasan Contoh Soal Nomor 3

BUKA Hint

Penyelesaian :

$\begin{align} ^6 \text{log 45} & = \dfrac{^3 \text{log 45}}{^3 \text{log 6}} \\ \\ & = \dfrac{^3 \text{log 3}^2\times 5}{^3 \text{log 3} \times 2} \\ \\ & = \dfrac{2 \times \, ^3\text{log 3} +^3\text{log 5}}{^3\text{log 3} + ^3\text{log 2}} \\ \\ & = \dfrac{2 \times 1 + b}{1 + \frac{1}{^2\text{log 3}}} \\ \\ & = \dfrac{2 + b}{1 + \frac{1}{a}} \\ \\ & = \dfrac{2 + b}{1 + \frac{1}{a}} \times \dfrac{a}{a}\\ \\ & = \bbox[5px,border:2px solid red]{ \dfrac {2a + ab}{a + 1} } \end{align}$

Contoh Soal Nomor 4

Diketahui $^2 \text{log 7} =a $ dan $^2 \text{log 3} = b$. Nilai $^6 \text{log 14}$ adalah ......

Pembahasan Contoh Soal Nomor 4

BUKA Hint

Penyelesaian :

$\begin{align} ^6 \text{log 14} & = \dfrac{^2 \text{log 14}}{^2 \text{log 6}} \\ \\ & = \dfrac{^2 \text{log 2}\times 7}{^2 \text{log 2} \times 3} \\ \\ & = \dfrac{^2\text{log 2} + ^2\text{log 7}}{^2\text{log 2} + ^2\text{log 3}} \\ \\ & = \bbox[5px,border:2px solid red]{ \dfrac {1 + a}{1 + b} } \end{align}$