Math / Algebra

Question $\ln \left(e^{-7}\right)=-7$ $A_{1}$ True B. False

Studdy Solution

STEP 1

1. The problem involves evaluating a natural logarithm.
2. The properties of logarithms and exponents will be used to verify the statement.

STEP 2

1. Understand the properties of logarithms and exponents.
2. Apply the properties to simplify the expression.
3. Verify the statement.

STEP 3

Recall the property of logarithms: The natural logarithm function, $\ln(x)$ , is the inverse of the exponential function $e^x$ . Therefore, $\ln(e^x) = x$ .

STEP 4

Apply the property of logarithms to simplify $\ln(e^{-7})$ :
According to the property $\ln(e^x) = x$ , we have:
$\ln(e^{-7}) = -7$

STEP 5

Verify the statement by comparing the simplified expression to the given equation:
The simplified expression $\ln(e^{-7}) = -7$ matches the given equation. Therefore, the statement is:
$A_{1} \text{ True}$
The statement is:
$A_{1} \text{ True}$

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Question $\ln \left(e^{-7}\right)=-7$ $A_{1}$ True B. False

Studdy Solution

STEP 1

1. The problem involves evaluating a natural logarithm.
2. The properties of logarithms and exponents will be used to verify the statement.

STEP 2

1. Understand the properties of logarithms and exponents.
2. Apply the properties to simplify the expression.
3. Verify the statement.

STEP 3

Recall the property of logarithms: The natural logarithm function, $\ln(x)$ , is the inverse of the exponential function $e^x$ . Therefore, $\ln(e^x) = x$ .

STEP 4

Apply the property of logarithms to simplify $\ln(e^{-7})$ :
According to the property $\ln(e^x) = x$ , we have:
$\ln(e^{-7}) = -7$

STEP 5

Verify the statement by comparing the simplified expression to the given equation:
The simplified expression $\ln(e^{-7}) = -7$ matches the given equation. Therefore, the statement is:
$A_{1} \text{ True}$
The statement is:
$A_{1} \text{ True}$

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Questionln⁡(e−7)=−7\ln \left(e^{-7}\right)=-7ln(e−7)=−7 A1A_{1}A1​ True B. False

Studdy Solution

STEP 1

1. The problem involves evaluating a natural logarithm.2. The properties of logarithms and exponents will be used to verify the statement.

STEP 2

1. Understand the properties of logarithms and exponents.2. Apply the properties to simplify the expression.3. Verify the statement.

STEP 3

Recall the property of logarithms: The natural logarithm function, ln⁡(x)\ln(x)ln(x), is the inverse of the exponential function exe^xex. Therefore, ln⁡(ex)=x\ln(e^x) = xln(ex)=x.

STEP 4

Apply the property of logarithms to simplify ln⁡(e−7)\ln(e^{-7})ln(e−7):According to the property ln⁡(ex)=x\ln(e^x) = xln(ex)=x, we have:ln⁡(e−7)=−7\ln(e^{-7}) = -7ln(e−7)=−7

STEP 5

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Question $\ln \left(e^{-7}\right)=-7$ $A_{1}$ True B. False

1. The problem involves evaluating a natural logarithm.
2. The properties of logarithms and exponents will be used to verify the statement.

1. Understand the properties of logarithms and exponents.
2. Apply the properties to simplify the expression.
3. Verify the statement.

Recall the property of logarithms: The natural logarithm function, $\ln(x)$ , is the inverse of the exponential function $e^x$ . Therefore, $\ln(e^x) = x$ .

Apply the property of logarithms to simplify $\ln(e^{-7})$ :
According to the property $\ln(e^x) = x$ , we have:
$\ln(e^{-7}) = -7$