Math / Algebra

QuestionEvaluating logarithmic expressions
Evaluate each expression. (a) $\log _{9} 1=$ $\square$ $\square$ Undefined $\square$

Studdy Solution

STEP 1

1. We are given the logarithmic expression $\log_{9} 1$ .
2. We need to evaluate this expression.

STEP 2

1. Recall the definition of a logarithm.
2. Apply the definition to the given expression.
3. Determine the value of the expression.

STEP 3

Recall the definition of a logarithm: $\log_{b} a = c$ means that $b^c = a$ .

STEP 4

Apply the definition to the given expression $\log_{9} 1$ .
We need to find the value of $c$ such that $9^c = 1$ .

STEP 5

Determine the value of $c$ .
Since any non-zero number raised to the power of 0 is 1, we have:
$9^0 = 1$
Thus, $c = 0$ .
The value of $\log_{9} 1$ is:
$\boxed{0}$

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QuestionEvaluating logarithmic expressions
Evaluate each expression. (a) $\log _{9} 1=$ $\square$ $\square$ Undefined $\square$

Studdy Solution

STEP 1

1. We are given the logarithmic expression $\log_{9} 1$ .
2. We need to evaluate this expression.

STEP 2

1. Recall the definition of a logarithm.
2. Apply the definition to the given expression.
3. Determine the value of the expression.

STEP 3

Recall the definition of a logarithm: $\log_{b} a = c$ means that $b^c = a$ .

STEP 4

Apply the definition to the given expression $\log_{9} 1$ .
We need to find the value of $c$ such that $9^c = 1$ .

STEP 5

Determine the value of $c$ .
Since any non-zero number raised to the power of 0 is 1, we have:
$9^0 = 1$
Thus, $c = 0$ .
The value of $\log_{9} 1$ is:
$\boxed{0}$

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QuestionEvaluating logarithmic expressionsEvaluate each expression. (a) log⁡91=\log _{9} 1=log9​1= □\square□ □\square□ Undefined □\square□

Studdy Solution

STEP 1

1. We are given the logarithmic expression log⁡91\log_{9} 1log9​1.2. We need to evaluate this expression.

STEP 2

1. Recall the definition of a logarithm.2. Apply the definition to the given expression.3. Determine the value of the expression.

STEP 3

Recall the definition of a logarithm: log⁡ba=c\log_{b} a = clogb​a=c means that bc=ab^c = abc=a.

STEP 4

Apply the definition to the given expression log⁡91\log_{9} 1log9​1.We need to find the value of ccc such that 9c=19^c = 19c=1.

STEP 5

Determine the value of ccc.Since any non-zero number raised to the power of 0 is 1, we have:90=1 9^0 = 1 90=1Thus, c=0c = 0c=0. The value of log⁡91\log_{9} 1log9​1 is:0 \boxed{0} 0​

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QuestionEvaluating logarithmic expressions
Evaluate each expression. (a) $\log _{9} 1=$ $\square$ $\square$ Undefined $\square$

1. We are given the logarithmic expression $\log_{9} 1$ .
2. We need to evaluate this expression.

1. Recall the definition of a logarithm.
2. Apply the definition to the given expression.
3. Determine the value of the expression.

Recall the definition of a logarithm: $\log_{b} a = c$ means that $b^c = a$ .

Apply the definition to the given expression $\log_{9} 1$ .
We need to find the value of $c$ such that $9^c = 1$ .

Determine the value of $c$ .
Since any non-zero number raised to the power of 0 is 1, we have:
$9^0 = 1$
Thus, $c = 0$ .
The value of $\log_{9} 1$ is:
$\boxed{0}$