Robert Bosch Logarithms Quiz 2

Answer: B
Explanation:
Using the logarithmic property, \log_x a = b can be rewritten as
x = a^b.
So, x = 6^{0.8} = 4.193.
So, Option B is closest to the answer.

Answer: -p
Explanation:
Using the logarithmic property,
\log_a \left(\frac{1}{b}\right) = -\log_a b.
Therefore, \log_5 \left(\frac{1}{25}\right) = -\log_5 25 = -p.

Answer: A) 6
Explanation:
\log_3 81 = \log_3 (3^4) = 4,
and \log_3 9 = \log_3 (3^2) = 2.
So, the sum is 4 + 2 = 6.

Answer: B) 1

Explanation: \log_7 49 = \log_7 (7^2) = 2,
and \log_7 7 = 1.
So, the difference is 2 - 1 = 1.

Answer: C
Explanation: Using the logarithmic property, \log_x a = b can be rewritten as x = a^b. So, x = 64^{\frac{3}{2}} = 16.

Answer: D) 7
Explanation:
\log_2 16 = \log_2 (2^4) = 4,
and \log_4 64 = \log_4 (4^3) = 3.
So, the sum is 4 + 3 = 7.

Answer: A) -\frac{2q}{3}
Explanation:
Using the logarithmic property,
\log_a \left(\frac{1}{b}\right) = -\log_a b.
Therefore, \log_3 \left(\frac{1}{9}\right) = -\log_3 9 = -2 \log_3 3 = -2.
So, the value in terms of q will be = -\frac{2q}{3} (Option A)

Answer: C
Explanation: [\log_4 (1/64)]^2 = [-\log_4 64]^2 = [-(-3)]^2 = (-3)^2 = 9.

Answer: B) 1
Explanation:
Using the logarithmic property, \log_a b^c = c \cdot \log_a b. Therefore, \log_a 6 = \log_a (2 \cdot 3) = \log_a 2 + \log_a 3 = 1 + 0 = 1.

Answer: B) 1

Explanation:
\log_5 125 = \log_5 (5^3) = 3, and \log_5 25 = \log_5 (5^2) = 2.
So, the difference is 3 - 2 = 1.