30 Questions
What is the condition on 'a' for y = loga x to be defined?
Any positive real number ≠ 1
What is the value of x in the equation 2^(2x) = 32^(5/4)?
3.6
Which of the following properties of logarithms is true?
loga b.logb a = 1
What is the value of loga (mn) if m and n are arbitrary positive numbers?
loga m + loga n
What can be said about the number log2 7?
It is an irrational number
What is the logarithm of a given number to a given base?
The index of the power to which the base must be raised in order to equal the given number
What is the range of the logarithmic function f(x) = loga x, a > 0, a ≠ 1?
R
What is the logarithmic identity that states a^(loga N) = N?
Fundamental logarithmic identity
If the characteristic of log10 N is -n, then how many zeros are there after the decimal part of N?
n-1
What is the logarithmic function called when the base is e?
Napierian logarithmic function
If log₇(2) = m, then log₄₉(28) is equal to?
2(1 + 2m)
If logₑ(a + b) = logₑ(a) + logₑ(b), then what is the relation between a and b?
a + b = ab
If log₁₀(3) = 0.477, then the number of digits in 3⁴⁰ is?
20
What is the correct order of the logarithms in increasing order for a given number α?
log₁₀(α), logₑ(α), log₂(α), log₃(α)
If y = 3⁴⁰, then what is the value of log(y)?
19.08
If logₐ(m) = logₐ(n) and a ≠ 1, then what can be concluded about m and n?
m = n
If logₐ(x) = p and logₐ(y) = q, then what is the value of logₐ(xy)?
p + q
Solve for x in the equation log₂(x) = 3/2.
√(2³)
If logₐ(b) = c and logₑ(d) = 1/c, then what is the value of logₑ(b)?
d
If a^(logₐ(m)) = m, then what is the value of m^(logₘ(a))?
a
What is the value of loga N if a^x = N and a^y = 1/N?
-x
If the logarithm of a number is 2.5, then what is the value of the number?
10^2.5
What is the value of loga MN if loga M = x and loga N = y?
x + y
If loga N = 2, then what is the value of log(a^2) N?
4
What is the value of loga (1/N) if loga N = x?
-x
If logₑ(x) + logₑ(y) = logₑ(z), then what is the relationship between x, y, and z?
xy = z
Solve for x in the equation log₂(x) = 2log₂(3) + log₂(4)
12
If loga(x) = loga(y) + loga(z), then what is the relationship between x, y, and z?
x = yz
If loga(x) = 2loga(y), then what is the relationship between x and y?
x = y^2
If log₂(x) = log₄(y), then what is the relationship between x and y?
x = y^(1/4)
Test your understanding of logarithms with these practice questions. Covers definition, logarithmic equations, and calculations.
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