LOGARITHM(LEVEL - 2)
Q1–10 of 50(log₅ 3) × (log₃ 625) equals
Using the base-change formula ($\log_b a = \frac{\log a}{\log b}$):
(log₅ 5)(log₄ 9)(log₃ 2) is equal to
$\log_5 5 \cdot \log_5 9 \cdot \log_3 2$
$\log_5 5 = 1$
$\log_5 9 = \log_5 (3^2) = 2 \log_5 3$
Multiply the terms:
If log₁₂ 27 = a, then log₆ 16 is
Since $\log_{12} (12) = \log_{12} (3 \times 4) = \log_{12} 3 + \log_{12} 4 = 1$:
We need $\log_{12} 16 = \log_{12} (4^2) = 2 \log_{12} 4$:
(To express in terms of base change, using $\log_{10}$):
Correct Option: (d)
If log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1, then x is equal to
If log₅ (x² + x) – log₅ (x + 1) = 2, then the value of x is
\( \dfrac{1}{2}(\log x+\log y)=\log\left(\dfrac{x+y}{2}\right) \)
if
$\frac{1}{2}(\log x + \log y) = \log\left(\frac{x+y}{2}\right)$
Correct Option: (c)
The value of
\( \dfrac{1}{\log_{3}60}+\dfrac{1}{\log_{4}60}+\dfrac{1}{\log_{5}60} \) is
Using reciprocal rule $\frac{1}{\log_a b} = \log_b a$:
Correct Option: (b)
The value of (log₃ 4)(log₄ 5)(log₅ 6)(log₆ 7)(log₇ 8)(log₈ 9) is
$(\log_3 4)(\log_4 5)(\log_5 6)(\log_6 7)(\log_7 8)(\log_8 9)$
Using the chain rule for logarithms:
Correct Option: (a)
The value of 16(log₄ 5) is.
Correct Option: (d)
If log x + log y = log (x + y), then
$\log x + \log y = \log(x+y)$
Correct Option: (d)