Logarithmic Functions: math test, Grade 11 – download the PDF

1 Conversions and values / 4 pts

1. Write \(5^3=125\) in logarithmic form.
2. Write \(\log_2\tfrac1{16}=-4\) in exponential form.
3. Evaluate \(\log_9 3\).
4. Evaluate \(\ln e^7+\log 1000\).

2 Properties of logarithms / 3 pts

1. Expand \(\log_3\dfrac{27x^2}{y}\).
2. Write \(3\ln 2+\ln 5-\ln 10\) as a single logarithm and simplify.

3 Exponential equations / 3 pts

Calculator allowed for part (b).

1. Solve \(6^{x-2}=216\).
2. Solve \(3\cdot 5^x=60\). Round to three decimal places.

4 Logarithmic equations / 4 pts

1. Solve \(\log_4(3x-2)=3\).
2. Solve \(\log_2 x+\log_2(x+6)=4\) and check your answers.

5 Reading a graph / 3 pts

The graph of a function \(f\) is shown. Its equation is \(f(x)=\log_3(x-1)+2\).

1. Give the domain of \(f\) and the equation of its asymptote.
2. Read the coordinates of the points A, B and C on the graph.
3. Compute \(f(28)\).

6 Acidity of solutions / 3 pts

The pH of a solution is \(\text{pH}=-\log[\text{H}^+]\), where \([\text{H}^+]\) is the hydrogen ion concentration in moles per liter. Calculator allowed.

1. Lemon juice has \([\text{H}^+]=2.5\times10^{-3}\). Find its pH to the nearest hundredth.
2. A solution has pH 8.3. Find \([\text{H}^+]\) in scientific notation with two significant digits.