Alg 2 Quiz 4.1

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  • CCSS.Math.Content.HSA-SSE.B.3
  • CCSS.Math.Content.HSF-LE.A.4
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Quizzes Created: 17 | Total Attempts: 12,896
| Attempts: 404 | Questions: 25 | Updated: Mar 19, 2025
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1) Write the given logarithmic equation in exponential form.log subscript 5 space 625 equals 4

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About This Quiz
Alg 2 Quiz 4.1 - Quiz

Alg 2 Quiz 4.1 assesses understanding of logarithmic and exponential forms. It includes transforming equations, condensing expressions, and solving real-world depreciation problems, enhancing skills in algebraic manipulations and practical applications.

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2) 23.  Write the given logarithmic equation in exponential form.log subscript 4.5 end subscript space 1 equals 0

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3) Write the given exponential equation in logarithmic form.6 to the power of x equals 216

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4) Write 4 to the power of 5 equals 1024 in logarithmic form

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5) Write the given logarithmic equation in exponential form.log subscript 2 space x equals 6

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The given logarithmic equation can be written in exponential form as follows: base^exponent = result.

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6) Write the given exponential equation in logarithmic form.4 to the power of negative 1 end exponent equals 0.25

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7) Write the given logarithmic equation in exponential form.log subscript 5 space x equals 4

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8) Which ordered pair lies on the graph y equals 0.8 open parentheses 2 to the power of x close parentheses?

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9) Rewrite the given logarithmic expression as a single logarithm.log space 2 space plus space log space x minus log space open parentheses x plus 3 close parentheses

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10) Which function represents exponential decay?

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Exponential decay is a mathematical function that describes a process in which a quantity decreases exponentially over time. In this case, the given answer states that none of the functions represent exponential decay. This suggests that there are no options provided that accurately represent the behavior of exponential decay.

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11) Write the given exponential equation in logarithmic form.x to the power of 2.5 end exponent equals 32

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12) Rewrite the exponential equation in logarithmic form.125 to the power of x equals 5

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13) Tony purchased a rare 1959 Gibson Les Paul guitar in 2000 for $12,000.  Experts estimate that its value will increase by 12% per year.  After how many years will the value have increased to $40,000?  Use A equals a left parenthesis 1 plus-or-minus r right parenthesis to the power of t.

Explanation

The value of the guitar increases by 12% each year, which means it grows by 0.12 times its previous value. To find the number of years it takes for the value to reach $40,000, we can set up the equation: $12,000 * (1 + 0.12)^n = $40,000. Solving for n, we find that it will take approximately 11.5 years for the value to increase to $40,000.

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14) Condense the given logarithmic expression into a single logarithm.log subscript 7 space 36 minus log subscript 7 space x

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15) Which function represents exponential growth?

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16) Rewrite the logarithmic expression as a single logarithm.log subscript 3 space 54 plus log subscript 3 space x space plus space log subscript 3 space 9

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17) The Allen Electric Company has a piece of machinery valued at $45,000.  It depreciates at 20% per year.  After how many years will the value have depreciated to $15,000?  Use A equals a left parenthesis 1 plus-or-minus r right parenthesis to the power of t.

Explanation

The value of the machinery depreciates at a rate of 20% per year. To find out how many years it will take for the value to depreciate to $15,000, we can set up the equation: $45,000 - (20% * $45,000 * x) = $15,000, where x represents the number of years. Simplifying the equation, we get $45,000 - (0.2 * $45,000 * x) = $15,000. Further simplifying, we have $45,000 - $9,000x = $15,000. Solving for x, we find that it will take 3 years for the value to depreciate to $15,000.

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18) Tonya invests $5000 in an account that pays 5% interest per year.  After how many years will her investment be worth $8000?  Use A equals a left parenthesis 1 plus-or-minus r right parenthesis to the power of t.

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19) The Allen Electric Company has a piece of machinery valued at $60,000.  It depreciates at 20% per year.  After how many years will the value have depreciated to $15,000?  Use A equals a left parenthesis 1 plus-or-minus r right parenthesis to the power of t.

Explanation

The value of the machinery depreciates at a rate of 20% per year. This means that each year, the value decreases by 20% of its current value. To find out how many years it will take for the value to depreciate to $15,000, we can set up an equation. Let "x" represent the number of years. The equation would be: $60,000 - (20% * $60,000 * x) = $15,000. By solving this equation, we can find the value of "x" which represents the number of years it will take for the machinery to depreciate to $15,000.

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20) Express as a single logarithm:3 space log subscript 5 space x space plus space log subscript 5 space y space minus space 2 space log subscript 5 space w

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21) Using the properties of logs, write in expanded form:log space open parentheses fraction numerator 2 a b over denominator c cubed end fraction close parentheses

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22) Using the properties of logs, write in expanded form:log space open square brackets open parentheses x minus 4 close parentheses open parentheses 2 x plus 5 close parentheses close square brackets squared

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23) If log subscript b space 4 equals k, then log subscript b space 16 is equivalent to:

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24) The expression log subscript a space open parentheses square root of a close parentheses to the power of k can be written as:

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25) The expression 3 plus log subscript 2 space x can be written as the single logarithm:

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Write the given logarithmic equation in exponential form.
23.  Write the given logarithmic equation in exponential form.
Write the given exponential equation in logarithmic form.
Write  in logarithmic form
Write the given logarithmic equation in exponential form.
Write the given exponential equation in logarithmic form.
Write the given logarithmic equation in exponential form.
Which ordered pair lies on the graph ?
Rewrite the given logarithmic expression as a single logarithm.
Which function represents exponential decay?
Write the given exponential equation in logarithmic form.
Rewrite the exponential equation in logarithmic form.
Tony purchased a rare 1959 Gibson Les Paul guitar in 2000 for $12,000....
Condense the given logarithmic expression into a single logarithm.
Which function represents exponential growth?
Rewrite the logarithmic expression as a single logarithm.
The Allen Electric Company has a piece of machinery valued at $45,000....
Tonya invests $5000 in an account that pays 5% interest per year....
The Allen Electric Company has a piece of machinery valued at $60,000....
Express as a single logarithm:
Using the properties of logs, write in expanded form:
Using the properties of logs, write in expanded form:
If , then  is equivalent to:
The expression  can be written as:
The expression  can be written as the single logarithm:
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