Simplified answer and explanation:
Q2: Simplify the equation x = log(2x) / log(7) rounded to the nearest ten thousandths.
Step 1: We can take the log of both sides: log(x) = log(log(2x) / log(7))
Step 2: According to the power rule of logs, we can bring down the 2x and multiply it by log(7) on the left-hand side of the equation: log(x) = (log(2x) / log(7)) * log(7) - log(2x)
Step 3: Divide both sides by log(7): log(x) / log(7) = log(2x) / log(7) - log(2x) / log(7)
Step 4: Divide both sides to both isolate and solve for x. Then round to the nearest ten thousandths: x = 0.6385
Answer: x = 0.6385
Q3: Simplify the equation for continuous compound interest: A(t) = P * e^(rt) rounded to the nearest hundredth for the interest rate as a percentage.
Step 1: Plug in everything we're already given to solve for r: P = 420, t = 6, and A(t) = 1300
Step 2: Divide both sides by 420: 1300 / 420 = e^(6r)
Step 3: Take the natural log (ln) of both sides: ln(1300 / 420) = 6r
Step 4: Bring down the 6r and multiply it by ln(e) on the right-hand side: ln(1300 / 420) = 6r * ln(e)
Step 5: Divide both sides by 6 to solve for r: r = ln(1300 / 420) / 6
Step 6: Convert the interest rate as a decimal to a percentage and round to the nearest hundredth: 18.83%
Answer: 18.83%
Q4: Convert to exponential form: 0.7^4 = 0.2401.
Answer: 0.7^4 = 0.2401
Q5: Simplify log(1250) to the nearest thousandth and ten thousandth.
Answer: log(1250) = 3.097 rounded to the nearest thousandth and 3.0969 rounded to the nearest ten thousandth.
Q6: Determine which statements are correct when two functions are inverses of each other.
Answer: Statements #1 and #2 are correct.
Q7: Solve for y using the change of base formula: y = log(0.125) / log(8).
Answer: y = -1
Q11: Find the x-intercept of the equation 0 = log(5x + 2) -1.
Step 1: Add 1 to both sides: 1 = log(5x + 2)
Step 2: Convert to exponential form and solve for x: 10^1 = 5x + 2, x = (10 - 2) / 5 = 1.6
Answer: x-intercept is 1.6.
Q12: False.
We set log argument equal to 0 and solve for find vertical asymptote. Solving 5x + 2 = 0, gives us vertical asymptote = x = -2/5
Q13:
Multiple numbers allowed:
- select 2. and 3. for the first function,select 1. and 4. for the second function,select 1. and 4. for the third function,and select 2. and 3. for the fourth function
One number allowed per function:
If you can only put 1 answer for each function, you can do
- 2. for the first function,1. for the second function,4. for the third function, and 3. for the fourth function