Math / Algebra

QuestionWrite the equation in exponential form.
8. $\log _{5} 125=3$
9. $\log _{625} 5=\frac{1}{4}$
10. $\log _{1 / 2} 64=-6$

Studdy Solution

STEP 1

What is this asking? We need to rewrite logarithm equations in their equivalent exponential forms. Watch out! Remember the relationship between logs and exponents: $\log_{b} a = c$ means $b^c = a$ .
Don't mix up the base, exponent, and result!

STEP 2

1. Convert Problem 8
2. Convert Problem 9
3. Convert Problem 10

STEP 3

We're given $\log_{5} 125 = 3$ .
Remember, a logarithm is just another way to write an exponent!

STEP 4

The base of our logarithm is $5$ , the result is $3$ , and the argument is $125$ .

STEP 5

Rewriting in exponential form gives us $5^3 = 125$ .
Boom!

STEP 6

We have $\log_{625} 5 = \frac{1}{4}$ .
Let's rock this conversion!

STEP 7

Our base is $625$ , the result is $\frac{1}{4}$ , and the argument is $5$ .

STEP 8

In exponential form, this becomes $625^{\frac{1}{4}} = 5$ .
Fractional exponents represent roots, so this makes sense!

STEP 9

We're given $\log_{1/2} 64 = -6$ .
Negative exponents?
No problem!

STEP 10

The base is $\frac{1}{2}$ , the result is $-6$ , and the argument is $64$ .

STEP 11

Rewriting gives us $(\frac{1}{2})^{-6} = 64$ .
Remember, a negative exponent flips the fraction!

STEP 12

Problem 8: $5^3 = 125$ Problem 9: $625^{\frac{1}{4}} = 5$ Problem 10: $(\frac{1}{2})^{-6} = 64$

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QuestionWrite the equation in exponential form.
8. $\log _{5} 125=3$
9. $\log _{625} 5=\frac{1}{4}$
10. $\log _{1 / 2} 64=-6$

Studdy Solution

STEP 1

What is this asking? We need to rewrite logarithm equations in their equivalent exponential forms. Watch out! Remember the relationship between logs and exponents: $\log_{b} a = c$ means $b^c = a$ .
Don't mix up the base, exponent, and result!

STEP 2

1. Convert Problem 8
2. Convert Problem 9
3. Convert Problem 10

STEP 3

We're given $\log_{5} 125 = 3$ .
Remember, a logarithm is just another way to write an exponent!

STEP 4

The base of our logarithm is $5$ , the result is $3$ , and the argument is $125$ .

STEP 5

Rewriting in exponential form gives us $5^3 = 125$ .
Boom!

STEP 6

We have $\log_{625} 5 = \frac{1}{4}$ .
Let's rock this conversion!

STEP 7

Our base is $625$ , the result is $\frac{1}{4}$ , and the argument is $5$ .

STEP 8

In exponential form, this becomes $625^{\frac{1}{4}} = 5$ .
Fractional exponents represent roots, so this makes sense!

STEP 9

We're given $\log_{1/2} 64 = -6$ .
Negative exponents?
No problem!

STEP 10

The base is $\frac{1}{2}$ , the result is $-6$ , and the argument is $64$ .

STEP 11

Rewriting gives us $(\frac{1}{2})^{-6} = 64$ .
Remember, a negative exponent flips the fraction!

STEP 12

Problem 8: $5^3 = 125$ Problem 9: $625^{\frac{1}{4}} = 5$ Problem 10: $(\frac{1}{2})^{-6} = 64$

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QuestionWrite the equation in exponential form.8. log⁡5125=3\log _{5} 125=3log5​125=39. log⁡6255=14\log _{625} 5=\frac{1}{4}log625​5=41​10. log⁡1/264=−6\log _{1 / 2} 64=-6log1/2​64=−6

Studdy Solution

STEP 1

What is this asking? We need to rewrite logarithm equations in their equivalent exponential forms. Watch out! Remember the relationship between logs and exponents: log⁡ba=c\log_{b} a = clogb​a=c means bc=ab^c = abc=a.Don't mix up the base, exponent, and result!

STEP 2

1. Convert Problem 82. Convert Problem 93. Convert Problem 10

STEP 3

We're given log⁡5125=3\log_{5} 125 = 3log5​125=3.Remember, a logarithm is just another way to write an exponent!

STEP 4

The **base** of our logarithm is 555, the **result** is 333, and the **argument** is 125125125.

STEP 5

Rewriting in exponential form gives us 53=1255^3 = 12553=125.Boom!

STEP 6

We have log⁡6255=14\log_{625} 5 = \frac{1}{4}log625​5=41​.Let's **rock** this conversion!

STEP 7

Our **base** is 625625625, the **result** is 14\frac{1}{4}41​, and the **argument** is 555.

STEP 8

In exponential form, this becomes 62514=5625^{\frac{1}{4}} = 562541​=5.Fractional exponents represent roots, so this makes sense!

STEP 9

We're given log⁡1/264=−6\log_{1/2} 64 = -6log1/2​64=−6.Negative exponents?No problem!

STEP 10

The **base** is 12\frac{1}{2}21​, the **result** is −6-6−6, and the **argument** is 646464.

STEP 11

Rewriting gives us (12)−6=64(\frac{1}{2})^{-6} = 64(21​)−6=64.Remember, a negative exponent flips the fraction!

STEP 12

Problem 8: 53=1255^3 = 12553=125 Problem 9: 62514=5625^{\frac{1}{4}} = 562541​=5 Problem 10: (12)−6=64(\frac{1}{2})^{-6} = 64(21​)−6=64

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Studdy solves anything!

Start learning now

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

QuestionWrite the equation in exponential form.
8. $\log _{5} 125=3$
9. $\log _{625} 5=\frac{1}{4}$
10. $\log _{1 / 2} 64=-6$

What is this asking? We need to rewrite logarithm equations in their equivalent exponential forms. Watch out! Remember the relationship between logs and exponents: $\log_{b} a = c$ means $b^c = a$ .
Don't mix up the base, exponent, and result!

1. Convert Problem 8
2. Convert Problem 9
3. Convert Problem 10

We're given $\log_{5} 125 = 3$ .
Remember, a logarithm is just another way to write an exponent!

The base of our logarithm is $5$ , the result is $3$ , and the argument is $125$ .

Rewriting in exponential form gives us $5^3 = 125$ .
Boom!

We have $\log_{625} 5 = \frac{1}{4}$ .
Let's rock this conversion!

Our base is $625$ , the result is $\frac{1}{4}$ , and the argument is $5$ .

In exponential form, this becomes $625^{\frac{1}{4}} = 5$ .
Fractional exponents represent roots, so this makes sense!

We're given $\log_{1/2} 64 = -6$ .
Negative exponents?
No problem!

The base is $\frac{1}{2}$ , the result is $-6$ , and the argument is $64$ .

Rewriting gives us $(\frac{1}{2})^{-6} = 64$ .
Remember, a negative exponent flips the fraction!

Problem 8: $5^3 = 125$ Problem 9: $625^{\frac{1}{4}} = 5$ Problem 10: $(\frac{1}{2})^{-6} = 64$