All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
2081
If log(x) = -1.5, how can this be written to show its characteristic and mantissa?
Answer:
2_bar.5000
Step 1: The mantissa must always be positive. -1.5 = -2 + 0.5. Step 2: The characteristic is -2, often written as 2_bar. Step 3: The mantissa is 0.5000. So the representation is 2_bar.5000.
2082
If log(3) = 0.4771, what is the value of log(300)?
Answer:
2.4771
Step 1: Express 300 in scientific notation or factor it: 300 = 3 * 100. Step 2: Use the product rule: log(300) = log(3) + log(100). Step 3: Substitute known values: 0.4771 + 2 = 2.4771.
2083
If log(2) = 0.3010, what is the value of log(8)?
Answer:
0.9030
Step 1: Write 8 as a power of 2: 8 = 2^3. Step 2: Substitute this into the logarithm: log(8) = log(2^3) = 3 * log(2). Step 3: Multiply the given value: 3 * 0.3010 = 0.9030.
2084
What is the characteristic of log(0.0073)?
Answer:
-3
Step 1: For a number N < 1, the characteristic is negative. Step 2: Count the number of zeros immediately after the decimal point and add 1. Make it negative. Step 3: 0.0073 has two zeros after the decimal point. So, -(2 + 1) = -3.
2085
What is the characteristic of log(456.7)?
Answer:
2
Step 1: The characteristic of a common logarithm is the integer part. Step 2: For a number N > 1, the characteristic is one less than the number of digits to the left of the decimal point. Step 3: 456.7 has 3 digits before the decimal. The characteristic is 3 - 1 = 2.
2086
Evaluate log(100) + log(0.1).
Answer:
1
Step 1: Evaluate log(100) which is log_10(10^2) = 2. Step 2: Evaluate log(0.1) which is log_10(10^-1) = -1. Step 3: Add the results: 2 + (-1) = 1.
2087
If 10^x = 40, find the exact value of x.
Answer:
log(40)
Step 1: The equation is in base 10. Take the common logarithm (log base 10) of both sides: log(10^x) = log(40). Step 2: Using the power rule, x * log(10) = log(40). Step 3: Since log(10) = 1, the equation simplifies exactly to x = log(40).
2088
Solve the exponential equation 3^x = 15. Express the answer using natural logarithms.
Answer:
ln(15) / ln(3)
Step 1: Take the natural logarithm (ln) of both sides: ln(3^x) = ln(15). Step 2: Use the power rule to bring x down: x * ln(3) = ln(15). Step 3: Divide both sides by ln(3) to isolate x: x = ln(15) / ln(3).
2089
Solve for x: log2(x) - log2(3) = 2.
Answer:
12
Step 1: Use the quotient rule to combine the logarithms: log2(x / 3) = 2. Step 2: Convert to exponential form: 2^2 = x / 3. Step 3: Simplify to 4 = x / 3, then multiply by 3 to get x = 12.
2090
Solve for x: log(x) + log(2) = log(14).
Answer:
7
Step 1: Use the product rule on the left side: log(x * 2) = log(14), so log(2x) = log(14). Step 2: Since the logarithmic function is one-to-one, we can equate the arguments: 2x = 14. Step 3: Divide by 2 to solve for x: x = 14 / 2 = 7.