Math / Algebra

QuestionRewrite each equation as requested. (a) Rewrite as a logarithmic equation. $2^{0}=1$ (b) Rewrite as an exponential equation. $\log _{5} \frac{1}{25}=-2$ (a) $\log _{\square} \square=$ $\square$ (b) $\square=$ $\square$

Studdy Solution

STEP 1

1. We need to convert between exponential and logarithmic forms.
2. The base of the exponential form becomes the base of the logarithm and vice versa.
3. The logarithm of a number is the exponent to which the base must be raised to produce that number.

STEP 2

1. Rewrite the given exponential equation as a logarithmic equation.
2. Rewrite the given logarithmic equation as an exponential equation.

STEP 3

Identify the base, exponent, and result in the exponential equation $2^{0} = 1$ .
The base is $2$ , the exponent is $0$ , and the result is $1$ .

STEP 4

Rewrite the exponential equation $2^{0} = 1$ as a logarithmic equation.
The logarithmic form is:
$\log_{2} 1 = 0$
This matches the format $\log_{\square} \square = \square$ .

STEP 5

Identify the base, result, and exponent in the logarithmic equation $\log_{5} \frac{1}{25} = -2$ .
The base is $5$ , the result is $\frac{1}{25}$ , and the exponent is $-2$ .

STEP 6

Rewrite the logarithmic equation $\log_{5} \frac{1}{25} = -2$ as an exponential equation.
The exponential form is:
$5^{-2} = \frac{1}{25}$
This matches the format $\square = \square$ .
The rewritten equations are: (a) $\log_{2} 1 = 0$ (b) $5^{-2} = \frac{1}{25}$

Was this helpful?

QuestionRewrite each equation as requested. (a) Rewrite as a logarithmic equation. $2^{0}=1$ (b) Rewrite as an exponential equation. $\log _{5} \frac{1}{25}=-2$ (a) $\log _{\square} \square=$ $\square$ (b) $\square=$ $\square$

Studdy Solution

STEP 1

1. We need to convert between exponential and logarithmic forms.
2. The base of the exponential form becomes the base of the logarithm and vice versa.
3. The logarithm of a number is the exponent to which the base must be raised to produce that number.

STEP 2

1. Rewrite the given exponential equation as a logarithmic equation.
2. Rewrite the given logarithmic equation as an exponential equation.

STEP 3

Identify the base, exponent, and result in the exponential equation $2^{0} = 1$ .
The base is $2$ , the exponent is $0$ , and the result is $1$ .

STEP 4

Rewrite the exponential equation $2^{0} = 1$ as a logarithmic equation.
The logarithmic form is:
$\log_{2} 1 = 0$
This matches the format $\log_{\square} \square = \square$ .

STEP 5

Identify the base, result, and exponent in the logarithmic equation $\log_{5} \frac{1}{25} = -2$ .
The base is $5$ , the result is $\frac{1}{25}$ , and the exponent is $-2$ .

STEP 6

Rewrite the logarithmic equation $\log_{5} \frac{1}{25} = -2$ as an exponential equation.
The exponential form is:
$5^{-2} = \frac{1}{25}$
This matches the format $\square = \square$ .
The rewritten equations are: (a) $\log_{2} 1 = 0$ (b) $5^{-2} = \frac{1}{25}$

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.

Studdy Solution

STEP 1

1. We need to convert between exponential and logarithmic forms.2. The base of the exponential form becomes the base of the logarithm and vice versa.3. The logarithm of a number is the exponent to which the base must be raised to produce that number.

STEP 2

1. Rewrite the given exponential equation as a logarithmic equation.2. Rewrite the given logarithmic equation as an exponential equation.

STEP 3

Identify the base, exponent, and result in the exponential equation 20=12^{0} = 120=1.The base is 222, the exponent is 000, and the result is 111.

STEP 4

Rewrite the exponential equation 20=12^{0} = 120=1 as a logarithmic equation.The logarithmic form is:log⁡21=0\log_{2} 1 = 0log2​1=0This matches the format log⁡□□=□\log_{\square} \square = \squarelog□​□=□.

STEP 5

Identify the base, result, and exponent in the logarithmic equation log⁡5125=−2\log_{5} \frac{1}{25} = -2log5​251​=−2.The base is 555, the result is 125\frac{1}{25}251​, and the exponent is −2-2−2.

STEP 6

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.

1. We need to convert between exponential and logarithmic forms.
2. The base of the exponential form becomes the base of the logarithm and vice versa.
3. The logarithm of a number is the exponent to which the base must be raised to produce that number.

1. Rewrite the given exponential equation as a logarithmic equation.
2. Rewrite the given logarithmic equation as an exponential equation.

Identify the base, exponent, and result in the exponential equation $2^{0} = 1$ .
The base is $2$ , the exponent is $0$ , and the result is $1$ .

Rewrite the exponential equation $2^{0} = 1$ as a logarithmic equation.
The logarithmic form is:
$\log_{2} 1 = 0$
This matches the format $\log_{\square} \square = \square$ .

Identify the base, result, and exponent in the logarithmic equation $\log_{5} \frac{1}{25} = -2$ .
The base is $5$ , the result is $\frac{1}{25}$ , and the exponent is $-2$ .