Algebra 2 | Unit 4 | Lesson 14: Solving Exponential Equations | Practice Problems

Solve each equation without using a calculator. Some solutions will need to be expressed using log notation. Solve 4 \times 10^x = 400,000

• x = 3

• x = 4

• x = 5

• x = 6

Solve each equation without using a calculator. Some solutions will need to be expressed using log notation. Solve 10^{(n+1)} = 1

• n = -1

• n = 0

• n = 1

• n = 2

Solve each equation without using a calculator. Some solutions will need to be expressed using log notation. Solve 10^{3n} = 1,000,000

• n = 0

• n = 1

• n = 2

• n = 3

Solve each equation without using a calculator. Some solutions will need to be expressed using log notation. Solve 10^p = 725

• p = ln 725

• p = log 725

• p = ln 626

• p = 725

Solve each equation without using a calculator. Some solutions will need to be expressed using log notation. Solve 6 \times 10^t = 360

• t = ln 60

• t = log 60

• t = ln 36

• t = 60

Solve \frac14 \times 10^{(d+2)} = 0.25. Show your reasoning.

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Write two equations—one in logarithmic form and one in exponential form—that represent the statement: “the natural logarithm of 10 is y”.

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Explain why ln 1 = 0.

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If log_{10}(x) = 6, what is the value of x? Explain how you know.

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For each logarithmic equation, write an equivalent equation in exponential form. log_2 16 = 4

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