LOGARITHM(LEVEL - 3)
Q1–10 of 50Find x, if log (2x – 3) = 2
(i) $\log 25$: $2(1 - \log 2) = 2(0.6990) = 1.398$.
(ii) $\log 4.5$: $\log(9/2) = 2\log 3 - \log 2 = 2(0.4771) - 0.3010 = 0.6532$.
Find x, if log 2ˣ = 3
Solution: Using the power rule of logarithms, $\log(2^x) = x \log 2 = 3$. Solving for $x$:
Correct Option: (c)
Find x, if 0.01ˣ = 2
Solution: Rewrite $0.01$ as $10^{-2}$. Taking $\log_{10}$ on both sides:
Correct Option: (d)
Find x if log x = log 7.2 – log 2.4
Solution: Applying the quotient rule $\log a - \log b = \log(a/b)$:
Correct Option: (c)
Solve the equation : log₁₅3375 × log₄1024 = ?
Solution: Note that $15^3 = 3375$ and $4^5 = 1024$.
Correct Option: (d)
Solve the equation : logₐ4 + logₐ16 + logₐ64 + logₐ256 = 10. Then a = ?
Solution: Combine using logarithmic product rule:
Correct Option: (a)
Solve the equation : log₆₂₅ √5 = ?
Solution: Express base and argument as powers of 5:
Correct Option: (c)
If log x + log (x + 3) = 1 then the value(s) of x will be, the solution of the equation
Solution: Combine the left side: $\log(x(x+3)) = 1$. Convert base 10 exponential form:
Correct Option: (c)
If log₁₀a = b, find the value of 10³ᵇ in terms of a.
Solution: From $\log_{10}a = b$, we get $10^b = a$. Thus:
Correct Option: (a)
Solve the equation : 3 log 5 + 2 log 4 – log 2 = ?
Solution: Apply exponent and product/quotient rules:
Correct Option: (b)