### All Common Core: High School - Functions Resources

## Example Questions

### Example Question #1 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

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 *d*are 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 value on one side of the equation.

Subtract two from both sides.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #2 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

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 *d*are 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 value on one side of the equation.

Subtract one from both sides.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #3 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

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 *d*are 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 value on one side of the equation.

Subtract one from both sides.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #4 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

*ab^(ct)* = *d* where *a*, *c*, and *d*are 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).

Subtract five from both sides and then divide by two.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #5 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

*ab^(ct)* = *d* where *a*, *c*, and *d*are 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).

Subtract five from both sides and then divide by four.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #6 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

*ab^(ct)* = *d* where *a*, *c*, and *d*are 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).

Subtract five from both sides and then divide by four.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #7 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

*ab^(ct)* = *d* where *a*, *c*, and *d*are 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).

Add six from both sides and then divide by four.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #61 : Linear, Quadratic, & Exponential Models*

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

*ab^(ct)* = *d* where *a*, *c*, and *d*are 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).

Add two from both sides.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #9 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

*ab^(ct)* = *d* where *a*, *c*, and *d*are 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).

Add one from both sides.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .

### Example Question #10 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

**Possible Answers:**

**Correct answer:**

*ab^(ct)* = *d* where *a*, *c*, and *d*are 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).

Add one from both sides.

Step 2: Identify logarithmic rules.

Recall that

Step 3: Apply logarithmic rules to solve for .