09.6 - Solving Logarithmic Equations
Quiz
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Easy
Standards-aligned
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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