**EXPONENTS AND LOGARITHMS, LAWS OF LOGARITHMS** **PROBLEM SET** **SINGLE CORRECT ANSWER TYPE** **LEVEL - 1** 1. Convert the following into exponential form $\log_a b = 39$ (A) $39^a$ (B) $a^b$ (C) $a^{39}$ (D) $39$ 2. Convert the following into logarithmic form $19^{x-1} = 2476099$ (A) $\log_{19} 2476099 = (x - 1)$ (B) $\log 2476099 = (x - 1)$ (C) $\log_x 2476099 = (x + 1)$ (D) $\log_{19} 2476099 = -(x - 1)$ 3. Find the value of $\log_{\sqrt{5}} \sqrt{125}$ (A) $3$ (B) $4$ (C) $6$ (D) $5$ 4. Find the value of $\log_5 (0.0028)$ (A) $4$ (B) $-4$ (C) $5$ (D) $-5$ 5. If $\log x + \log x^2 + \log x^3 = 9$, then $x$ equals to (A) $3$ (B) $9$ (C) $27$ (D) none of these 6. If $a, b, c$ are positive real numbers, then $2^{\log a - \log b} \cdot 2^{\log b - \log c} \cdot 2^{\log c - \log a} =$ (A) $0$ (B) $1$ (C) $-1$ (D) none of these 7. If $x = \log_a a, y = \log_{2a} 2a$ and $z = \log_{3a} 3a$, then $xyz + 1 =$ (A) $2yz$ (B) $2xy$ (C) $2zx$ (D) none of these 8. If $a = \log 2, b = \log 3, c = \log 7$ and $6^x = 7^{x+4}$, then $x =$ (A) $\frac{4b}{c + a - b}$ (B) $\frac{4c}{a + b - c}$ (C) $\frac{4b}{c - a - b}$ (D) $\frac{4a}{a + b - c}$ 9. If $a = 1 + \log_x yz, b = 1 + \log_y zx, c = 1 + \log_z xy$, then $ab + bc + ca =$ (A) $0$ (B) $2abc$ (C) $abc$ (D) $a^2 + b^2 + c^2$ 10. If $x = 27$ and $y = \log_3 4$, then $x^y$ equals (A) $64$ (B) $16$ (C) $\frac{3}{7}$ (D) $\frac{1}{16}$ 11. If $\log_2 128 =$ (A) $\frac{7}{3}$ (B) $16$ (C) $\frac{3}{7}$ (D) $\frac{1}{16}$ 12. Logarithm of unity to any non-zero base is (A) Non-zero number (B) Unity (C) $0$ (D) $-1$ 13. $\log_2 7$ is (A) an integer (B) a rational number (C) an irrational number (D) a prime number

Answer: 1 (Option B)

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