#1
What is the logarithm of 1000 with base 10?
4
ExplanationLogarithm of a number expresses the power to which a given base must be raised to produce that number.
#2
Simplify log(base 2)(8) + log(base 2)(2).
4
ExplanationAdding logarithms of the same base corresponds to multiplication of the numbers.
#3
What is the value of log(base 5)(125)?
3
ExplanationLogarithm represents the exponent required to produce the given value with the given base.
#4
Solve for x: log(base 5)(x) = 2.
25
ExplanationLogarithmic equations can be solved by isolating the variable and applying the inverse operation.
#5
What is the value of log(base 4)(64)?
3
ExplanationLogarithm represents the exponent required to produce the given value with the given base.
#6
What is the value of log(base 3)(27)?
3
ExplanationLogarithm is the exponent to which the base must be raised to produce the given value.
#7
If log(base 10)(x) = 2, what is the value of x?
100
ExplanationLogarithmic equations can be solved by expressing them in exponential form.
#8
What is the logarithmic form of the equation 3^2 = 9?
log(9, 3) = 2
ExplanationLogarithmic form expresses the relationship between exponentiation and logarithms.
#9
If log(base x)(8) = 3, what is the value of x?
2
ExplanationLogarithmic equations can be solved by transforming them into exponential form.
#10
If log(base 2)(x) = 3, what is the value of x?
16
ExplanationLogarithmic equations can be solved by expressing them in exponential form.
#11
Which property states that log(a*b) = log(a) + log(b)?
Product Rule
ExplanationProduct Rule simplifies the logarithm of a product into the sum of the logarithms.
#12
Which property states that log(a/b) = log(a) - log(b)?
Quotient Rule
ExplanationQuotient Rule simplifies the logarithm of a quotient into the difference of the logarithms.
#13
If log(base 2)(x) = 5 and log(base 2)(y) = 3, what is log(base 2)(x*y)?
8
ExplanationProduct Rule allows the multiplication inside the logarithm to be represented as the sum of logarithms.
#14
Evaluate log(base 4)(2) + log(base 4)(8).
2
ExplanationAdding logarithms of the same base corresponds to multiplication of the numbers.
#15
Evaluate log(base 3)(9) - log(base 3)(3).
1
ExplanationSubtracting logarithms of the same base corresponds to division of the numbers.