Podcast
Questions and Answers
What is the condition on 'a' for y = loga x to be defined?
What is the condition on 'a' for y = loga x to be defined?
- Any positive real number ≠ 1 (correct)
- Any number
- Any positive real number
- Any positive real number > 1
What is the value of x in the equation 2^(2x) = 32^(5/4)?
What is the value of x in the equation 2^(2x) = 32^(5/4)?
- 3.6 (correct)
- 5.6
- None of these
- 4.5
Which of the following properties of logarithms is true?
Which of the following properties of logarithms is true?
- loga b = logb a
- loga b.logb a = 1 (correct)
- loga b.logc a = logc b
- loga b.logb c = loga c
What is the value of loga (mn) if m and n are arbitrary positive numbers?
What is the value of loga (mn) if m and n are arbitrary positive numbers?
What can be said about the number log2 7?
What can be said about the number log2 7?
What is the logarithm of a given number to a given base?
What is the logarithm of a given number to a given base?
What is the range of the logarithmic function f(x) = loga x, a > 0, a ≠ 1?
What is the range of the logarithmic function f(x) = loga x, a > 0, a ≠ 1?
What is the logarithmic identity that states a^(loga N) = N?
What is the logarithmic identity that states a^(loga N) = N?
If the characteristic of log10 N is -n, then how many zeros are there after the decimal part of N?
If the characteristic of log10 N is -n, then how many zeros are there after the decimal part of N?
What is the logarithmic function called when the base is e?
What is the logarithmic function called when the base is e?
If log₇(2) = m, then log₄₉(28) is equal to?
If log₇(2) = m, then log₄₉(28) is equal to?
If logₑ(a + b) = logₑ(a) + logₑ(b), then what is the relation between a and b?
If logₑ(a + b) = logₑ(a) + logₑ(b), then what is the relation between a and b?
If log₁₀(3) = 0.477, then the number of digits in 3⁴⁰ is?
If log₁₀(3) = 0.477, then the number of digits in 3⁴⁰ is?
What is the correct order of the logarithms in increasing order for a given number α?
What is the correct order of the logarithms in increasing order for a given number α?
If y = 3⁴⁰, then what is the value of log(y)?
If y = 3⁴⁰, then what is the value of log(y)?
If logₐ(m) = logₐ(n) and a ≠ 1, then what can be concluded about m and n?
If logₐ(m) = logₐ(n) and a ≠ 1, then what can be concluded about m and n?
If logₐ(x) = p and logₐ(y) = q, then what is the value of logₐ(xy)?
If logₐ(x) = p and logₐ(y) = q, then what is the value of logₐ(xy)?
Solve for x in the equation log₂(x) = 3/2.
Solve for x in the equation log₂(x) = 3/2.
If logₐ(b) = c and logₑ(d) = 1/c, then what is the value of logₑ(b)?
If logₐ(b) = c and logₑ(d) = 1/c, then what is the value of logₑ(b)?
If a^(logₐ(m)) = m, then what is the value of m^(logₘ(a))?
If a^(logₐ(m)) = m, then what is the value of m^(logₘ(a))?
What is the value of loga N if a^x = N and a^y = 1/N?
What is the value of loga N if a^x = N and a^y = 1/N?
If the logarithm of a number is 2.5, then what is the value of the number?
If the logarithm of a number is 2.5, then what is the value of the number?
What is the value of loga MN if loga M = x and loga N = y?
What is the value of loga MN if loga M = x and loga N = y?
If loga N = 2, then what is the value of log(a^2) N?
If loga N = 2, then what is the value of log(a^2) N?
What is the value of loga (1/N) if loga N = x?
What is the value of loga (1/N) if loga N = x?
If logₑ(x) + logₑ(y) = logₑ(z), then what is the relationship between x, y, and z?
If logₑ(x) + logₑ(y) = logₑ(z), then what is the relationship between x, y, and z?
Solve for x in the equation log₂(x) = 2log₂(3) + log₂(4)
Solve for x in the equation log₂(x) = 2log₂(3) + log₂(4)
If loga(x) = loga(y) + loga(z), then what is the relationship between x, y, and z?
If loga(x) = loga(y) + loga(z), then what is the relationship between x, y, and z?
If loga(x) = 2loga(y), then what is the relationship between x and y?
If loga(x) = 2loga(y), then what is the relationship between x and y?
If log₂(x) = log₄(y), then what is the relationship between x and y?
If log₂(x) = log₄(y), then what is the relationship between x and y?
