Logarithms and Logarithmic Functions: Algebra 2 Math Test – PDF Download

Question 1: Convert forms (2 points)

1. Write \(5^{3}=125\) in logarithmic form. (1 point)
2. Write \(\log_{9} 3=\frac{1}{2}\) in exponential form. (1 point)

Question 2: Evaluate logs (2 points)

1. Evaluate \(\log_{3} 243\). (1 point)
2. Evaluate \(\log 0.0001\). (1 point)

Question 3: Graph of a logarithm (3 points)

The graph of \(f(x)=\log_{2}(x+3)-1\) is shown.

1. Write the equation of the vertical asymptote. (1 point)
2. State the domain and the range. (1 point)
3. Find the x-intercept algebraically. (1 point)

Question 4: Domain (2 points)

1. Find the domain of \(f(x)=\ln(4x-12)\). (1 point)
2. Find the domain of \(g(x)=\log_{5}(7-x)\). (1 point)

Question 5: Properties of logs (2 points)

1. Expand \(\log_{2}\frac{8x^{2}}{y}\). (1 point)
2. Find the exact value of \(2\log 5+\log 4\). (1 point)

Question 6: Change of base (2 points)

Evaluate \(\log_{7} 30\) to the nearest thousandth. Show the setup.

Question 7: Inverse function (3 points)

The function \(f(x)=3^{x}+4\) is graphed.

1. Find \(f^{-1}(x)\). (2 points)
2. Find \(f^{-1}(31)\). (1 point)

Question 8: Acidity (2 points)

Use \(\text{pH}=-\log[H^{+}]\).

1. Lemon juice has \([H^{+}]=0.0063\) mol/L. Find its pH to the nearest hundredth. (1 point)
2. A solution has pH 8.4. Find \([H^{+}]\) in scientific notation with three significant digits. (1 point)

Question 9: Sound intensity (2 points)

Sound level is \(L=10\log\frac{I}{I_{0}}\) decibels.

1. Find \(\frac{I}{I_{0}}\) when \(L=70\). (1 point)
2. Find \(L\) to the nearest tenth when \(\frac{I}{I_{0}}=5\times 10^{8}\). (1 point)

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