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Common Core: High School - Functions : Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

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Example Questions

Example Question #341 : High School: Functions

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

$e^{x-4}-1=0$ $\displaystyle e^{x-4}-1=0$

Possible Answers:

x=2 $\displaystyle x=2$

$x=\ln2$ $\displaystyle x=\ln2$

x=3 $\displaystyle x=3$

$x=\ln1$ $\displaystyle x=\ln1$

x=4 $\displaystyle x=4$

Correct answer:

x=4 $\displaystyle x=4$

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.

$e^{x-4}-1=0$ $\displaystyle e^{x-4}-1=0$

Add one from both sides.

$\\e^{x-4}-1+1=0+1 \\e^{x-4}=1$ $\displaystyle \\e^{x-4}-1+1=0+1 \\e^{x-4}=1$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$ $\displaystyle \ln e=1$ and $\ln1=0$ $\displaystyle \ln1=0$

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

$\\e^{x-4}=1 \\ \ln e^{x-4}=\ln 1\\ x-4=\ln 1\\x=\ln 1+4\\x=0+4\\x=4$ $\displaystyle \\e^{x-4}=1 \\ \ln e^{x-4}=\ln 1\\ x-4=\ln 1\\x=\ln 1+4\\x=0+4\\x=4$

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Common Core: High School - Functions : Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #341 : High School: Functions

All Common Core: High School - Functions Resources

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