Math / Algebra

QuestionWrite the following using the log base change rule, and change to either log base 10 (write log) or log base e (write it as In) $\log _{2}(7)$

Studdy Solution

STEP 1

1. We need to express $\log_{2}(7)$ using the change of base formula.
2. We can choose to convert it to either base 10 logarithm (log) or natural logarithm (ln).

STEP 2

1. Apply the change of base formula to $\log_{2}(7)$ .
2. Express the result using either log base 10 or log base e.

STEP 3

Apply the change of base formula, which states:
$\log_{b}(a) = \frac{\log_{k}(a)}{\log_{k}(b)}$
where $k$ is the new base. Here, $b = 2$ and $a = 7$ .

STEP 4

Choose to express $\log_{2}(7)$ using log base 10:
$\log_{2}(7) = \frac{\log(7)}{\log(2)}$

STEP 5

Alternatively, express $\log_{2}(7)$ using natural logarithm (ln):
$\log_{2}(7) = \frac{\ln(7)}{\ln(2)}$
The expression $\log_{2}(7)$ can be written as either $\frac{\log(7)}{\log(2)}$ or $\frac{\ln(7)}{\ln(2)}$ .

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QuestionWrite the following using the log base change rule, and change to either log base 10 (write log) or log base e (write it as In) $\log _{2}(7)$

Studdy Solution

STEP 1

1. We need to express $\log_{2}(7)$ using the change of base formula.
2. We can choose to convert it to either base 10 logarithm (log) or natural logarithm (ln).

STEP 2

1. Apply the change of base formula to $\log_{2}(7)$ .
2. Express the result using either log base 10 or log base e.

STEP 3

Apply the change of base formula, which states:
$\log_{b}(a) = \frac{\log_{k}(a)}{\log_{k}(b)}$
where $k$ is the new base. Here, $b = 2$ and $a = 7$ .

STEP 4

Choose to express $\log_{2}(7)$ using log base 10:
$\log_{2}(7) = \frac{\log(7)}{\log(2)}$

STEP 5

Alternatively, express $\log_{2}(7)$ using natural logarithm (ln):
$\log_{2}(7) = \frac{\ln(7)}{\ln(2)}$
The expression $\log_{2}(7)$ can be written as either $\frac{\log(7)}{\log(2)}$ or $\frac{\ln(7)}{\ln(2)}$ .

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QuestionWrite the following using the log base change rule, and change to either log base 10 (write log) or log base e (write it as In) log⁡2(7)\log _{2}(7)log2​(7)

Studdy Solution

STEP 1

1. We need to express log⁡2(7)\log_{2}(7)log2​(7) using the change of base formula.2. We can choose to convert it to either base 10 logarithm (log) or natural logarithm (ln).

STEP 2

1. Apply the change of base formula to log⁡2(7)\log_{2}(7)log2​(7).2. Express the result using either log base 10 or log base e.

STEP 3

Apply the change of base formula, which states:log⁡b(a)=log⁡k(a)log⁡k(b)\log_{b}(a) = \frac{\log_{k}(a)}{\log_{k}(b)}logb​(a)=logk​(b)logk​(a)​where kkk is the new base. Here, b=2b = 2b=2 and a=7a = 7a=7.

STEP 4

Choose to express log⁡2(7)\log_{2}(7)log2​(7) using log base 10:log⁡2(7)=log⁡(7)log⁡(2)\log_{2}(7) = \frac{\log(7)}{\log(2)}log2​(7)=log(2)log(7)​

STEP 5

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QuestionWrite the following using the log base change rule, and change to either log base 10 (write log) or log base e (write it as In) $\log _{2}(7)$

1. We need to express $\log_{2}(7)$ using the change of base formula.
2. We can choose to convert it to either base 10 logarithm (log) or natural logarithm (ln).

1. Apply the change of base formula to $\log_{2}(7)$ .
2. Express the result using either log base 10 or log base e.

Apply the change of base formula, which states:
$\log_{b}(a) = \frac{\log_{k}(a)}{\log_{k}(b)}$
where $k$ is the new base. Here, $b = 2$ and $a = 7$ .

Choose to express $\log_{2}(7)$ using log base 10:
$\log_{2}(7) = \frac{\log(7)}{\log(2)}$