Math / Algebra

QuestionFind the logarithm. $\log (10,000)=$

Studdy Solution

STEP 1

1. We are working with the common logarithm, which is base 10.
2. We need to find the value of $\log_{10} (10,000)$ .

STEP 2

1. Express $10,000$ as a power of 10.
2. Use the properties of logarithms to find the solution.

STEP 3

Express $10,000$ as a power of 10:
$10,000 = 10^4$

STEP 4

Use the property of logarithms that states $\log_{10} (10^n) = n$ :
$\log_{10} (10,000) = \log_{10} (10^4)$

STEP 5

Apply the property:
$\log_{10} (10^4) = 4$
The value of $\log (10,000)$ is:
$\boxed{4}$

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QuestionFind the logarithm. $\log (10,000)=$

Studdy Solution

STEP 1

1. We are working with the common logarithm, which is base 10.
2. We need to find the value of $\log_{10} (10,000)$ .

STEP 2

1. Express $10,000$ as a power of 10.
2. Use the properties of logarithms to find the solution.

STEP 3

Express $10,000$ as a power of 10:
$10,000 = 10^4$

STEP 4

Use the property of logarithms that states $\log_{10} (10^n) = n$ :
$\log_{10} (10,000) = \log_{10} (10^4)$

STEP 5

Apply the property:
$\log_{10} (10^4) = 4$
The value of $\log (10,000)$ is:
$\boxed{4}$

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QuestionFind the logarithm. log⁡(10,000)=\log (10,000)=log(10,000)=

Studdy Solution

STEP 1

1. We are working with the common logarithm, which is base 10.2. We need to find the value of log⁡10(10,000)\log_{10} (10,000)log10​(10,000).

STEP 2

1. Express 10,00010,00010,000 as a power of 10.2. Use the properties of logarithms to find the solution.

STEP 3

Express 10,00010,00010,000 as a power of 10:10,000=104 10,000 = 10^4 10,000=104

STEP 4

Use the property of logarithms that states log⁡10(10n)=n\log_{10} (10^n) = nlog10​(10n)=n:log⁡10(10,000)=log⁡10(104) \log_{10} (10,000) = \log_{10} (10^4) log10​(10,000)=log10​(104)

STEP 5

Apply the property:log⁡10(104)=4 \log_{10} (10^4) = 4 log10​(104)=4 The value of log⁡(10,000)\log (10,000)log(10,000) is:4 \boxed{4} 4​

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QuestionFind the logarithm. $\log (10,000)=$

1. We are working with the common logarithm, which is base 10.
2. We need to find the value of $\log_{10} (10,000)$ .

1. Express $10,000$ as a power of 10.
2. Use the properties of logarithms to find the solution.

Express $10,000$ as a power of 10:
$10,000 = 10^4$

Use the property of logarithms that states $\log_{10} (10^n) = n$ :
$\log_{10} (10,000) = \log_{10} (10^4)$

Apply the property:
$\log_{10} (10^4) = 4$
The value of $\log (10,000)$ is:
$\boxed{4}$