change of Base Formula

Exam 4 Name: ________________________________ Show all your work for full credit: 100 points Part 1: 65 points (in class) Part 2: 35 points (take home) Part 1: 1 Q1. (9 points) A) Write the equation 64βˆ’1/2 = 8 in logarithmic form. B) Use the change of Base Formula to evaluate π‘™π‘œπ‘”2 6 C) Use the Laws of Logarithms to expand the expression. 4π‘₯ 2 log ( 𝑦3 ) Q2. (8 points) Solve the equation. Find the exact solution and rounded to two decimal places. 31βˆ’π‘₯ = 52π‘₯ 1 Exam 4 Name: ________________________________ Show all your work for full credit: 100 points Q3. (8 points) Solve the equation. Find the exact solution. π‘™π‘œπ‘”2 (π‘₯ βˆ’ 7) + π‘™π‘œπ‘”2 π‘₯ = 3 Q4. (8 points) Suppose that $8,000 is invested in a saving account paying 5% interest per year. How long will it take for the amount in the account to grow to $16,000 if interest is compounded quarterly? 2 Exam 4 Name: ________________________________ Show all your work for full credit: 100 points Q5. (10 points) a) Sketch the graph of the function. State its domain, range in the interval notation. State its asymptote. Show the π‘₯ βˆ’ and 𝑦 βˆ’intercepts on the graph. 𝑓(π‘₯) = 3π‘₯ + 2 3 Exam 4 Name: ________________________________ Show all your work for full credit: 100 points Q6. (10 points) Radiumβ€”221 has a half-life of 30s. Suppose we have a 300 g sample. a) Find a formula for the mass remaining after t seconds. b) How much of the sample remains after 200 seconds? c) After how long will only 20 g remain? 4 Exam 4 Name: ________________________________ Show all your work for full credit: 100 points Q7. (12 points) a) b) c) d) e) Sketch the graph of the function. State its domain, range in the interval notation State its asymptote. Show the π‘₯ βˆ’ and 𝑦 βˆ’intercepts on the graph. Graph 𝑓 βˆ’1 (π‘₯) on the same graph as part (a) Find 𝑓 βˆ’1 (π‘₯) 𝑓(π‘₯) = π‘™π‘œπ‘”2 (π‘₯ + 4) + 2 5
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