Solving Exponential and Logarithmic Equations: Algebra 2 Math Test – PDF Download

Question 1: Common base (2 points)

1. Solve \(3^{2x-1}=81\). (1 point)
2. Solve \(5^{x+2}=\frac{1}{25}\). (1 point)

Question 2: Solve with logarithms (2 points)

1. Solve \(6^{x}=90\). Round to three decimal places. (1 point)
2. Solve \(e^{0.4x}=14\). Round to three decimal places. (1 point)

Question 3: Logarithmic equations (2 points)

1. Solve \(\log_{3}(2x+1)=4\). (1 point)
2. Solve \(\ln(x-2)=1.5\). Round to three decimal places. (1 point)

Question 4: Combine logarithms (3 points)

Solve \(\log_{2} x+\log_{2}(x+2)=3\). The graph of the left side is shown with the line \(y=3\).

1. Write the equation without logarithms. (1 point)
2. Solve the equation. (1 point)
3. Identify any extraneous solution and explain why. (1 point)

Question 5: Quotient of logarithms (2 points)

Solve \(\log_{5}(3x+2)-\log_{5} x=1\).

Question 6: Quadratic form (2 points)

Solve \(3^{2x}-10\cdot 3^{x}+9=0\).

Question 7: Compound interest (3 points)

Priya deposits \$2,500 at 3.6% compounded monthly. The balance is \(A=2500(1+\frac{0.036}{12})^{12t}\) after \(t\) years.

1. Write the equation for the time when the balance is \$4,000. (1 point)
2. Solve it. Round to the nearest hundredth of a year. (2 points)

Question 8: Half-life (2 points)

A 120 g sample of iodine-131 has half-life 8 days, so \(N(t)=120(\frac{1}{2})^{t/8}\).

1. When do 15 g remain? (1 point)
2. When do 40 g remain? Round to the nearest hundredth of a day. (1 point)

Question 9: Equivalent forms (2 points)

A balance grows as \(P(t)=800(1.06)^{t}\). (a) Write \(P\) as \(800e^{kt}\) and give \(k\) to four decimal places. (1 point) (b) Find the equivalent monthly growth rate as a percent to three decimal places. (1 point)

⬇ Download the Algebra 2 Solving Exponential and Logarithmic Equations test (PDF, 93 KB)

See every chapter on the Algebra 2 math page.