Quiz about Mudança de Base de Logaritmos

Question 1

Converta $$\log_5 25$$ para a base 10.

Accepted Answer

$$\frac{\log_{10} 25}{\log_{10} 5}$$

Answer

$$\frac{\log_{10} 5}{\log_{10} 25}$$

Answer

$$\log_{10} 25 \cdot \log_{10} 5$$

Answer

$$\log_{10} (25 + 5)$$

Question 2

Converta $$\log_7 49$$ para a base 2.

Accepted Answer

$$\frac{\log_{2} 49}{\log_{2} 7}$$

Answer

$$\frac{\log_{7} 2}{\log_{49} 2}$$

Answer

$$\frac{\log_{2} 7}{\log_{2} 49}$$

Answer

$$\log_{2} (49 + 7)$$

Question 3

Converta $$\log_9 3$$ para a base 10.

Accepted Answer

$$\frac{\log_{10} 3}{\log_{10} 9}$$

Answer

$$\frac{\log_{10} 9}{\log_{10} 3}$$

Answer

$$\log_{10} (9 + 3)$$

Answer

$$\log_{10} (9 \cdot 3)$$

Question 4

Converta $$\log_6 36$$ para a base 3.

Accepted Answer

$$\frac{\log_{3} 36}{\log_{3} 6}$$

Answer

$$\frac{\log_{6} 3}{\log_{36} 3}$$

Answer

$$\frac{\log_{3} 6}{\log_{3} 36}$$

Answer

$$\log_{3} (36 - 6)$$

Question 5

Converta $$\log_2 16$$ para a base $$e$$ (logaritmo natural).

Accepted Answer

$$\frac{\ln 16}{\ln 2}$$

Answer

$$\frac{\ln 2}{\ln 16}$$

Answer

$$\ln (16 + 2)$$

Answer

$$\ln (16 \cdot 2)$$

Question 6

Converta $$\log_4 2$$ para a base 10.

Accepted Answer

$$\frac{\log_{10} 2}{\log_{10} 4}$$

Answer

$$\frac{\log_{10} 4}{\log_{10} 2}$$

Answer

$$\log_{10} (4 + 2)$$

Answer

$$\log_{10} (4 \cdot 2)$$

Question 7

Converta $$\log_{12} 144$$ para a base 3.

Accepted Answer

$$\frac{\log_{3} 144}{\log_{3} 12}$$

Answer

$$\frac{\log_{3} 12}{\log_{3} 144}$$

Answer

$$\log_{3} (144 + 12)$$

Answer

$$\log_{3} (144 \cdot 12)$$

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