09.6 - Solving Logarithmic Equations

09.6 - Solving Logarithmic Equations

9th - 12th Grade

20 Qs

quiz-placeholder

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09.6 - Solving Logarithmic Equations

09.6 - Solving Logarithmic Equations

Assessment

Quiz

Mathematics

9th - 12th Grade

Practice Problem

Easy

CCSS
HSF.LE.A.4, HSF.BF.B.5

Standards-aligned

Created by

Denise Lum

Used 1+ times

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20 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Answer explanation

To solve the equation \(10^x = 42\), we take the logarithm base 10 of both sides, yielding \(x = \log_{10}(42)\). This is the correct choice, approximately equal to 1.623.

Tags

CCSS.HSF.BF.B.5

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Answer explanation

To solve for x in the equation 8^x = 0.00325, we use logarithms. The correct form is x = log_8(0.00325). Calculating this gives approximately -2.755, confirming the first answer choice as correct.

Tags

CCSS.HSF.BF.B.5

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

0.987

2.133

3.456

1.234

Answer explanation

To solve for x, rewrite the equation as 10^{5-3x} = 0.041. Taking the logarithm gives 5 - 3x = log10(0.041). Solving for x yields x = (5 - log10(0.041))/3, which approximates to 2.133.

Tags

CCSS.HSF.LE.A.4

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

5.123

7.890

2.961

6.267

Answer explanation

To solve for x in the equation 3^{x+1}=2007, take the logarithm of both sides: (x+1) log(3) = log(2007). Solving gives x ≈ 2.961, which matches the correct answer choice.

Tags

CCSS.HSF.LE.A.4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

3.682

3.879

2.500

4.000

Answer explanation

To solve the equation 2·5^x - 29 = 1000, first add 29 to both sides to get 2·5^x = 1029. Then divide by 2, yielding 5^x = 514.5. Taking the logarithm gives x = log(514.5)/log(5) ≈ 3.879, which is the correct answer.

Tags

CCSS.HSF.LE.A.4

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

3.332204

2.718281

4.000000

3.000000

Answer explanation

To solve for x, rearrange the equation: e^x = 40 - 12 = 28. Taking the natural logarithm gives x = ln(28). This evaluates to approximately 3.332204, which is the correct answer.

Tags

CCSS.HSF.LE.A.4

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

3.884

5.225

4.125

6.350

Answer explanation

To solve for x, first isolate e^x: 5e^x = 843, then e^x = 168.6. Taking the natural logarithm gives x = ln(168.6) ≈ 3.884. Thus, the correct answer is 3.884.

Tags

CCSS.HSF.LE.A.4

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