• A. $\frac{13}{12}{\log }_{e^x}$
• B. ${\log }_{e^x}$
• C. $\frac{1}{2}{\log }_{e^x}$
• D. ${\log }_e\sqrt{x}$

Answer: Option A

Explanation:

• A. 1
• B. 2
• C. 3
• D. 4

Answer: Option C

Explanation:

• A. $32$
• B. $40$
• C. $48$
• D. $80$

Answer: Option B

Explanation:

• A. $a>0,a\ne 1$
• B. $a\text{not 0, a>1}$
• C. $a>0,a=0$
• D. $a not 0 1, a>0$

Answer: Option A

Explanation:

• A. 8 log a
• B. 28 log a
• C. 38 log a
• D. 48 log a

Answer: Option B

Explanation:

• A. $\frac{4}{9}$
• B. $\frac{9}{4}$
• C. $\sqrt{\frac{3}{2}}$
• D. $\sqrt{\frac{2}{3}}$

Answer: Option A

Explanation:

• A. $\frac{-1}{3}$
• B. $-3$
• C. $\frac{1}{3}$
• D. $3$

Answer: Option C

Explanation:

• A. $45\log 2$
• B. $55\log 2$
• C. $65\log 2$
• D. $75\log 2$

Answer: Option B

Explanation:

• A. 4
• B. 5
• C. 8
• D. 20

Answer: Option A

Explanation:

• A. 2
• B. 3
• C. -2
• D. -3

Answer: Option C

Explanation:

• A. 1
• B. 1/5
• C. 5/6
• D. 6/5

Answer: Option C

Explanation:

• A. $2$
• B. $\sqrt{2}$
• C. $2\sqrt{2}$
• D. $4$

Answer: Option C

Explanation:

• A. $\frac{1}{25}$
• B. -5
• C. $\frac{1}{5}$
• D. $\frac{-1}{5}$

Answer: Option B

Explanation:

• A. $10$
• B. $e$
• C. $2$
• D. $2\sqrt{5}$

Answer: Option D

Explanation:

• A. $1$
• B. $4$
• C. $2$
• D. $5$

Answer: Option B

Explanation: