LOGARITHM(LEVEL - 1)
Q1–10 of 50The value of log₂ 16 is
Solution: $\log_{2}(2^4) = 4\log_{2}2 = 4(1) = 4$.
Correct Option: (b)
The value of log₃₄₃ 7 is
Solution: $\log_{7^3} 7 = \frac{1}{3}\log_{7}7 = \frac{1}{3}$.
Correct Option: (a
The value of log₅ \( \dfrac{(125)(625)}{25} \) is equal to
Solution: $\log_{7^3} 7 = \frac{1}{3}\log_{7}7 = \frac{1}{3}$.
Correct Option: (a
The value of log√2 32 is.
Solution: $\log_{2^{1/2}}(2^5) = \frac{5}{1/2}\log_2 2 = 10$.
Correct Option: (c)
Determine the value of log 3√2 (1/18)
Solution: $(3\sqrt{2})^2 = 9 \times 2 = 18$. Thus, $\frac{1}{18} = (3\sqrt{2})^{-2}$. Therefore, $\log_{3\sqrt{2}}((3\sqrt{2})^{-2}) = -2$.
Correct Option: (b)
The value of log₁₀ (.0001) is
Solution: $0.0001 = 10^{-4} \implies \log_{10}(10^{-4}) = -4$.
Correct Option: (c)
The value of log.₀₁ (1000) is
Solution: $\log_{10^{-2}}(10^3) = \frac{3}{-2} = -\frac{3}{2}$.
Correct Option: (d)
What is the value of [log₁₀ (5 log₁₀ 100)]²?
Solution: $\log_{10} 100 = 2 \implies \log_{10}(5 \times 2) = \log_{10} 10 = 1$. Then $1^2 = 1$.
Correct Option: (a)
The logarithm of 0.0625 to the base 2 is
Solution: $0.0625 = \frac{625}{10000} = \frac{1}{16} = 2^{-4} \implies \log_2(2^{-4}) = -4$.
Correct Option: (a)
The logarithm of 0.00001 to the base 0.01 is equal to
Solution: $\log_{10^{-2}}(10^{-5}) = \frac{-5}{-2} = \frac{5}{2}$.
Correct Option: (b)