QuestionFind the exact value of the expression using logarithm properties: $\log_{3} 6 - \log_{3} 2$ .

Studdy Solution

STEP 1

Assumptions1. We are using the properties of logarithms to solve the problem. . The base of the logarithms is3.
3. We are not using a calculator.

STEP 2

We can use the property of logarithms that states the difference of two logarithms is the logarithm of the quotient of their arguments.
$\log_b a - \log_b c = \log_b \left(\frac{a}{c}\right)$

STEP 3

Apply this property to the given expression.
$\log{3}6-\log{3}2 = \log{3} \left(\frac{6}{2}\right)$

STEP 4

implify the fraction inside the logarithm.
$\log{3} \left(\frac{6}{2}\right) = \log{3}3$

STEP 5

The logarithm of a number with the same base is1. Therefore,
$\log{3}3 =1$ So, the exact value of the expression is1.

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QuestionFind the exact value of the expression using logarithm properties: $\log_{3} 6 - \log_{3} 2$ .

Studdy Solution

STEP 1

Assumptions1. We are using the properties of logarithms to solve the problem. . The base of the logarithms is3.
3. We are not using a calculator.

STEP 2

We can use the property of logarithms that states the difference of two logarithms is the logarithm of the quotient of their arguments.
$\log_b a - \log_b c = \log_b \left(\frac{a}{c}\right)$

STEP 3

Apply this property to the given expression.
$\log{3}6-\log{3}2 = \log{3} \left(\frac{6}{2}\right)$

STEP 4

implify the fraction inside the logarithm.
$\log{3} \left(\frac{6}{2}\right) = \log{3}3$

STEP 5

The logarithm of a number with the same base is1. Therefore,
$\log{3}3 =1$ So, the exact value of the expression is1.

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QuestionFind the exact value of the expression using logarithm properties: log⁡36−log⁡32\log_{3} 6 - \log_{3} 2log3​6−log3​2.

Studdy Solution

STEP 1

Assumptions1. We are using the properties of logarithms to solve the problem. . The base of the logarithms is3.3. We are not using a calculator.

STEP 2

We can use the property of logarithms that states the difference of two logarithms is the logarithm of the quotient of their arguments.log⁡ba−log⁡bc=log⁡b(ac)\log_b a - \log_b c = \log_b \left(\frac{a}{c}\right)logb​a−logb​c=logb​(ca​)

STEP 3

Apply this property to the given expression.log⁡36−log⁡32=log⁡3(62)\log{3}6-\log{3}2 = \log{3} \left(\frac{6}{2}\right)log36−log32=log3(26​)

STEP 4

implify the fraction inside the logarithm.log⁡3(62)=log⁡33\log{3} \left(\frac{6}{2}\right) = \log{3}3log3(26​)=log33

STEP 5

The logarithm of a number with the same base is1. Therefore,log⁡33=1\log{3}3 =1log33=1So, the exact value of the expression is1.

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QuestionFind the exact value of the expression using logarithm properties: $\log_{3} 6 - \log_{3} 2$ .

Assumptions1. We are using the properties of logarithms to solve the problem. . The base of the logarithms is3.
3. We are not using a calculator.

We can use the property of logarithms that states the difference of two logarithms is the logarithm of the quotient of their arguments.
$\log_b a - \log_b c = \log_b \left(\frac{a}{c}\right)$

Apply this property to the given expression.
$\log{3}6-\log{3}2 = \log{3} \left(\frac{6}{2}\right)$

implify the fraction inside the logarithm.
$\log{3} \left(\frac{6}{2}\right) = \log{3}3$

The logarithm of a number with the same base is1. Therefore,
$\log{3}3 =1$ So, the exact value of the expression is1.