Math / Algebra

Questionsion $\log _{8} z=6$ is written in the logarithmic form $a^{b}=c$ , $b=$ and $c=$

Studdy Solution

STEP 1

1. The given equation is in logarithmic form: $\log_{8} z = 6$ .
2. We need to convert this logarithmic equation into its equivalent exponential form $a^{b} = c$ .

STEP 2

1. Identify the base, exponent, and result in the logarithmic equation.
2. Write the equivalent exponential form.
3. Determine the values of $b$ and $c$ .

STEP 3

Identify the components of the logarithmic equation $\log_{8} z = 6$ : - The base $a$ is 8. - The result of the logarithm is $z$ . - The exponent $b$ is 6.

STEP 4

Convert the logarithmic equation into its equivalent exponential form using the identified components. The general conversion is $\log_{a} c = b$ to $a^{b} = c$ :
$8^{6} = z$

STEP 5

Determine the values of $b$ and $c$ from the exponential form: - $b = 6$ - $c = z$
The values are: $b = 6$ $c = z$

Was this helpful?

Questionsion $\log _{8} z=6$ is written in the logarithmic form $a^{b}=c$ , $b=$ and $c=$

Studdy Solution

STEP 1

1. The given equation is in logarithmic form: $\log_{8} z = 6$ .
2. We need to convert this logarithmic equation into its equivalent exponential form $a^{b} = c$ .

STEP 2

1. Identify the base, exponent, and result in the logarithmic equation.
2. Write the equivalent exponential form.
3. Determine the values of $b$ and $c$ .

STEP 3

Identify the components of the logarithmic equation $\log_{8} z = 6$ : - The base $a$ is 8. - The result of the logarithm is $z$ . - The exponent $b$ is 6.

STEP 4

Convert the logarithmic equation into its equivalent exponential form using the identified components. The general conversion is $\log_{a} c = b$ to $a^{b} = c$ :
$8^{6} = z$

STEP 5

Determine the values of $b$ and $c$ from the exponential form: - $b = 6$ - $c = z$
The values are: $b = 6$ $c = z$

Get Studdy

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.

Questionsion log⁡8z=6\log _{8} z=6log8​z=6 is written in the logarithmic form ab=ca^{b}=cab=c, b=b=b= and c=c=c=

Studdy Solution

STEP 1

1. The given equation is in logarithmic form: log⁡8z=6\log_{8} z = 6log8​z=6.2. We need to convert this logarithmic equation into its equivalent exponential form ab=ca^{b} = cab=c.

STEP 2

1. Identify the base, exponent, and result in the logarithmic equation.2. Write the equivalent exponential form.3. Determine the values of bbb and ccc.

STEP 3

Identify the components of the logarithmic equation log⁡8z=6\log_{8} z = 6log8​z=6: - The base aaa is 8. - The result of the logarithm is zzz. - The exponent bbb is 6.

STEP 4

Convert the logarithmic equation into its equivalent exponential form using the identified components. The general conversion is log⁡ac=b\log_{a} c = bloga​c=b to ab=ca^{b} = cab=c:86=z 8^{6} = z 86=z

STEP 5

Determine the values of bbb and ccc from the exponential form: - b=6b = 6b=6 - c=zc = zc=z The values are: b=6 b = 6 b=6 c=z c = z c=z

Get Studdy

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.

Questionsion $\log _{8} z=6$ is written in the logarithmic form $a^{b}=c$ , $b=$ and $c=$

1. The given equation is in logarithmic form: $\log_{8} z = 6$ .
2. We need to convert this logarithmic equation into its equivalent exponential form $a^{b} = c$ .

1. Identify the base, exponent, and result in the logarithmic equation.
2. Write the equivalent exponential form.
3. Determine the values of $b$ and $c$ .

Identify the components of the logarithmic equation $\log_{8} z = 6$ : - The base $a$ is 8. - The result of the logarithm is $z$ . - The exponent $b$ is 6.

Convert the logarithmic equation into its equivalent exponential form using the identified components. The general conversion is $\log_{a} c = b$ to $a^{b} = c$ :
$8^{6} = z$

Determine the values of $b$ and $c$ from the exponential form: - $b = 6$ - $c = z$
The values are: $b = 6$ $c = z$