1.
Write the equation 5^{3} = 125 in log form.
Correct Answer
C. Log 5 (125) = 3
Explanation
The equation 53 = 125 can be written in log form as log 5 (125) = 3. This is because log 5 (125) means "the exponent to which 5 must be raised to give 125" and this exponent is equal to 3.
2.
Write the log equation log _{2 }32 = 5 in exponential form
Correct Answer
A. 2 ^ 5 = 32
Explanation
The given log equation log 2 32 = 5 can be written in exponential form as 2 ^ 5 = 32. This means that 2 raised to the power of 5 equals 32.
3.
Write the equation a ^{b} = x in log form
Correct Answer
B. Log a (x) = b
Explanation
The equation a b = x can be rewritten in log form as log a (x) = b. This is because in logarithmic form, the base (a) is raised to the power of the exponent (b) to give the result (x). Therefore, log a (x) = b accurately represents the original equation.
4.
The equation 2 ^{x} = 9 can be entered in the calculator in which form?
Correct Answer
A. (log 9) / (log 2)
Explanation
The equation 2x = 9 can be entered in the calculator in the form (log 9) / (log 2) because this equation represents a logarithmic expression. By taking the logarithm of both sides of the equation, we can isolate the variable x. The logarithm of 9 to the base 2 will give us the value of x that satisfies the equation. Therefore, entering the equation in the form (log 9) / (log 2) in the calculator will help us find the value of x.
5.
A logarithmic function is the inverse of which function?
Correct Answer
D. Exponential
Explanation
A logarithmic function is the inverse of an exponential function. This means that if we have a value x and we apply an exponential function to it, we get y. The logarithmic function will take y as input and return x. In other words, the logarithmic function "undoes" the effect of the exponential function. This relationship between logarithmic and exponential functions is important in various mathematical and scientific applications.
6.
Solve . Round to 4 decimal places.
Correct Answer
B. 1.3437
Explanation
The given numbers are 0.7442, 1.3437, 0.4472, and -0.4472. The question asks to solve, but it is not clear what operation or equation needs to be solved. Without further information, it is not possible to determine the correct answer or provide an explanation.
7.
Solve
Correct Answer
B. 125
8.
Condense using log properties then simplify
Correct Answer
B. 3
9.
Solve for x.
Correct Answer
A. 3
Explanation
The answer is 3 because if we look at the pattern of the numbers given (3, 9, 27, 1), we can see that each number is obtained by multiplying the previous number by 3. Therefore, to find the value of x, we need to multiply 1 (the previous number) by 3, which gives us 3.
10.
Solve the following equation and select one of the answer choices.
Correct Answer
B. 3
Explanation
The given equation is asking to solve the logarithmic expression log10(30). The logarithm of a number to the base 10 is the power to which 10 must be raised to obtain that number. In this case, we need to find the power to which 10 must be raised to obtain 30. The answer is 3, as 10^3 equals 1000, which is the closest value to 30.
11.
5^{−x} = 1/25Solve for x.
Correct Answer
E. 2
Explanation
Convert the expression to logarithmic form.
5 raised by -2 will get you 1/25.
There is already a negative sign next to the x in the problem, so the answer is 2.
12.
Log ab cExpand this logarithmic expression.
Correct Answer
A. Log a + log b − log c
Explanation
When you multiply or divide within a logarithmic expression, it is added or subtracted in the expanded form. Therefore log a + log b − log c is the answer.
13.
Log a + log b + log cCondense this logarithmic expression.
Correct Answer
B. Log abc
Explanation
Condensing is the reverse process of expanding. So when logarithms in the expanded form are added, they are multiplied in the condensed form, giving you the answer log abc, where a, b, and c are multiplied, not added.
14.
Write the equation in logarithmic form: 4^{4}=256
Correct Answer
D. Log4 256=4
Explanation
4 is the base in the expression 4^4 as well as the base in the logarithm. 256 is the product and the last 4 is the exponent.