Math / Algebra

QuestionUse a calculator to find the common logarithm. $\log (22)$
The answer is $\square$ . (Round to four decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We need to find the base-10 logarithm of $22$ and round it to four decimal places. Watch out! Make sure your calculator is set to base-10 logarithm and not natural logarithm (base- $e$ ).
Also, don't forget to round correctly!

STEP 2

1. Calculate the logarithm.
2. Round the result.

STEP 3

When we say $\log(22)$ , we're asking: "10 raised to what power equals $22$ ?".
Since $10^1 = 10$ and $10^2 = 100$ , we know the answer will be between $1$ and $2$ .

STEP 4

Using a calculator, we find that $\log(22) \approx 1.34242268082$ .
This tells us that $10$ raised to the power of approximately $1.34242268082$ equals $22$ .

STEP 5

Our calculated value is $1.34242268082$ .
The fifth decimal place is $2$ .

STEP 6

Since the fifth decimal place ( $2$ ) is less than $5$ , we round down, meaning we keep the fourth decimal place as it is.

STEP 7

Rounding to four decimal places, we get $1.3424$ .
So, $\log(22) \approx 1.3424$ .

STEP 8

The common logarithm of $22$ , rounded to four decimal places, is $1.3424$ .

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QuestionUse a calculator to find the common logarithm. $\log (22)$
The answer is $\square$ . (Round to four decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We need to find the base-10 logarithm of $22$ and round it to four decimal places. Watch out! Make sure your calculator is set to base-10 logarithm and not natural logarithm (base- $e$ ).
Also, don't forget to round correctly!

STEP 2

1. Calculate the logarithm.
2. Round the result.

STEP 3

When we say $\log(22)$ , we're asking: "10 raised to what power equals $22$ ?".
Since $10^1 = 10$ and $10^2 = 100$ , we know the answer will be between $1$ and $2$ .

STEP 4

Using a calculator, we find that $\log(22) \approx 1.34242268082$ .
This tells us that $10$ raised to the power of approximately $1.34242268082$ equals $22$ .

STEP 5

Our calculated value is $1.34242268082$ .
The fifth decimal place is $2$ .

STEP 6

Since the fifth decimal place ( $2$ ) is less than $5$ , we round down, meaning we keep the fourth decimal place as it is.

STEP 7

Rounding to four decimal places, we get $1.3424$ .
So, $\log(22) \approx 1.3424$ .

STEP 8

The common logarithm of $22$ , rounded to four decimal places, is $1.3424$ .

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QuestionUse a calculator to find the common logarithm. log⁡(22)\log (22)log(22)The answer is □\square□ . (Round to four decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We need to find the base-10 logarithm of 222222 and round it to four decimal places. Watch out! Make sure your calculator is set to base-10 logarithm and not natural logarithm (base-eee).Also, don't forget to round correctly!

STEP 2

1. Calculate the logarithm.2. Round the result.

STEP 3

When we say log⁡(22)\log(22)log(22), we're asking: "10 raised to what power equals 222222?".Since 101=1010^1 = 10101=10 and 102=10010^2 = 100102=100, we know the answer will be between 111 and 222.

STEP 4

Using a calculator, we find that log⁡(22)≈1.34242268082\log(22) \approx 1.34242268082log(22)≈1.34242268082.This tells us that 101010 raised to the power of approximately 1.342422680821.342422680821.34242268082 equals 222222.

STEP 5

Our calculated value is 1.342422680821.342422680821.34242268082.The fifth decimal place is 222.

STEP 6

Since the fifth decimal place (222) is less than 555, we round down, meaning we keep the fourth decimal place as it is.

STEP 7

Rounding to four decimal places, we get 1.34241.34241.3424.So, log⁡(22)≈1.3424\log(22) \approx 1.3424log(22)≈1.3424.

STEP 8

The common logarithm of 222222, rounded to four decimal places, is 1.34241.34241.3424.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionUse a calculator to find the common logarithm. $\log (22)$
The answer is $\square$ . (Round to four decimal places as needed.)

What is this asking? We need to find the base-10 logarithm of $22$ and round it to four decimal places. Watch out! Make sure your calculator is set to base-10 logarithm and not natural logarithm (base- $e$ ).
Also, don't forget to round correctly!

1. Calculate the logarithm.
2. Round the result.

When we say $\log(22)$ , we're asking: "10 raised to what power equals $22$ ?".
Since $10^1 = 10$ and $10^2 = 100$ , we know the answer will be between $1$ and $2$ .

Using a calculator, we find that $\log(22) \approx 1.34242268082$ .
This tells us that $10$ raised to the power of approximately $1.34242268082$ equals $22$ .

Our calculated value is $1.34242268082$ .
The fifth decimal place is $2$ .

Since the fifth decimal place ( $2$ ) is less than $5$ , we round down, meaning we keep the fourth decimal place as it is.

Rounding to four decimal places, we get $1.3424$ .
So, $\log(22) \approx 1.3424$ .

The common logarithm of $22$ , rounded to four decimal places, is $1.3424$ .