1.
Logarithm properties must have the same base to be simplified.
Correct Answer
A. True
Explanation
Logarithm properties state that logarithms with the same base can be simplified. This means that if two logarithms have the same base, they can be combined into a single logarithm using the properties of logarithms. This simplification allows for easier calculations and manipulation of logarithmic expressions. Therefore, the statement in the question is true.
2.
The logarithm of a quotient is the logarithm of the dividend.
Correct Answer
A. True
Explanation
The statement is true because according to the logarithmic property of division, the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. In other words, when dividing two numbers, the logarithm of the quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Therefore, the logarithm of a quotient is indeed the logarithm of the dividend.
3.
The log of 73 to the base 7 is 8/4.
Correct Answer
B. False
Explanation
The statement is false because the log of 73 to the base 7 is not equal to 8/4. The correct answer is false because the logarithm of a number to a specific base is a single value, not a fraction. In this case, the log of 73 to the base 7 would be a single number, not a fraction like 8/4.
4.
The log of 62 to the base 6 is 5/4.
Correct Answer
B. False
Explanation
The statement is false because the logarithm of a number to a certain base cannot result in a fractional value. The logarithm of 62 to the base 6 would be a whole number, not a fraction like 5/4.
5.
Find the log of 32 to the base 4.
Correct Answer
C. 5/2
Explanation
The logarithm of a number to a certain base is the exponent to which the base must be raised to obtain that number. In this case, we need to find the exponent to which 4 must be raised to obtain 32. Since 4^2 = 16 and 4^3 = 64, we can see that 32 is between 16 and 64. Therefore, the logarithm of 32 to the base 4 is between 2 and 3. The only option that falls between 2 and 3 is 5/2.
6.
Find x if log_{5}(x-7)=1.
Correct Answer
A. 12
Explanation
The equation log5(x-7)=1 can be rewritten as 5^1 = x-7. Simplifying further, we get x-7=5. Adding 7 to both sides of the equation, we find x=12.
7.
Rewrite 3^{4} = 81 in logarithmic form.
Correct Answer
C. Log_{3}81 = 4
Explanation
The given equation "log381 = 4" is the correct answer. In logarithmic form, it means that the logarithm of 381 to the base 3 is equal to 4.
8.
Logarithms are the opposite of the inverse of exponents.
Correct Answer
B. False
Explanation
The statement "Logarithms are the opposite of the inverse of exponents" is not correct. Logarithms and exponents are related, but they are not opposites. In fact, logarithms help us solve for exponents. Logarithms are used to find the exponent that a base must be raised to in order to obtain a certain number. So, the correct answer is False.
9.
Change to Exponential Form:
log_{6}36 = 2
Correct Answer
B. 6^{2}=36
10.
Rewrite log_{p}t = m in exponential form.
Correct Answer
D. P^{m} = t
Explanation
The given equation is logpt = m. To rewrite it in exponential form, we need to isolate the base (p) and the exponent (m). By raising both sides to the power of p, we get pt = m. Therefore, the correct answer is pm = t, as it represents the exponential form of the given equation.