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Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Solve for $\displaystyle x$ using rules of logarithmic functions.

$e^{x-4}+2=10$ $\displaystyle e^{x-4}+2=10$

$x=\ln 8-4$ $\displaystyle x=\ln 8-4$

$x=\frac{\ln 8}{4}$ $\displaystyle x=\frac{\ln 8}{4}$

$x={\ln 4}$ $\displaystyle x={\ln 4}$

$x=\frac{\ln 8}{2}$ $\displaystyle x=\frac{\ln 8}{2}$

$x=\ln 8+4$ $\displaystyle x=\ln 8+4$

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Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Solve for $\displaystyle x$ using rules of logarithmic functions.

$e^{x-4}+2=10$ $\displaystyle e^{x-4}+2=10$

$x=\ln 8-4$ $\displaystyle x=\ln 8-4$

$x=\frac{\ln 8}{4}$ $\displaystyle x=\frac{\ln 8}{4}$

$x={\ln 4}$ $\displaystyle x={\ln 4}$

$x=\frac{\ln 8}{2}$ $\displaystyle x=\frac{\ln 8}{2}$

$x=\ln 8+4$ $\displaystyle x=\ln 8+4$

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Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Solve for $\displaystyle x$ using rules of logarithmic functions.

$e^{x-4}+2=10$ $\displaystyle e^{x-4}+2=10$

Your answer:

$x=\ln 8-4$ $\displaystyle x=\ln 8-4$

Your answer:

$x=\frac{\ln 8}{4}$ $\displaystyle x=\frac{\ln 8}{4}$

Your answer:

$x={\ln 4}$ $\displaystyle x={\ln 4}$

Your answer:

$x=\frac{\ln 8}{2}$ $\displaystyle x=\frac{\ln 8}{2}$

Correct answer:

$x=\ln 8+4$ $\displaystyle x=\ln 8+4$

Explanation:

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and dare numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the $\displaystyle x$ value on one side of the equation.

$e^{x-4}+2=10$ $\displaystyle e^{x-4}+2=10$

Subtract two from both sides.

$\\e^{x-4}+2-2=10-2 \\e^{x-4}=8$ $\displaystyle \\e^{x-4}+2-2=10-2 \\e^{x-4}=8$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$ $\displaystyle \ln e=1$

Step 3: Apply logarithmic rules to solve for $\displaystyle x$ .

$\\e^{x-4}=8 \\ \ln e^{x-4}=\ln 8\\ x-4=\ln 8\\x=\ln 8+4$ $\displaystyle \\e^{x-4}=8 \\ \ln e^{x-4}=\ln 8\\ x-4=\ln 8\\x=\ln 8+4$

Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Solve for $\displaystyle x$ using rules of logarithmic functions.

$e^{x-4}+1=5$ $\displaystyle e^{x-4}+1=5$

$x=\ln4-4$ $\displaystyle x=\ln4-4$

$x=\ln4-1$ $\displaystyle x=\ln4-1$

$x=\ln4+1$ $\displaystyle x=\ln4+1$

$x=\ln4+4$ $\displaystyle x=\ln4+4$

$x=\ln1+4$ $\displaystyle x=\ln1+4$

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Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Solve for $\displaystyle x$ using rules of logarithmic functions.

$e^{x-4}+1=5$ $\displaystyle e^{x-4}+1=5$

Your answer:

$x=\ln4-4$ $\displaystyle x=\ln4-4$

Your answer:

$x=\ln4-1$ $\displaystyle x=\ln4-1$

Your answer:

$x=\ln4+1$ $\displaystyle x=\ln4+1$

Your answer:

$x=\ln1+4$ $\displaystyle x=\ln1+4$

Correct answer:

$x=\ln4+4$ $\displaystyle x=\ln4+4$

Explanation:

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the $\displaystyle x$ value on one side of the equation.

$e^{x-4}+1=5$ $\displaystyle e^{x-4}+1=5$

Subtract one from both sides.

$\\e^{x-4}+1-1=5-1 \\e^{x-4}=4$ $\displaystyle \\e^{x-4}+1-1=5-1 \\e^{x-4}=4$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$ $\displaystyle \ln e=1$

Step 3: Apply logarithmic rules to solve for $\displaystyle x$ .

$\\e^{x-4}=4 \\ \ln e^{x-4}=\ln 4\\ x-4=\ln 4\\x=\ln 4+4$ $\displaystyle \\e^{x-4}=4 \\ \ln e^{x-4}=\ln 4\\ x-4=\ln 4\\x=\ln 4+4$

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Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

All Common Core: High School - Functions Resources

Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Flashcards: Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

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