Math / Algebra

QuestionWrite in logarithmic form. $\frac{1}{256} = 4^{-4}$ The logarithmic form is $\boxed{}$ . (Use integers or fractions for any numbers in the expression.)

Studdy Solution

STEP 1

What is this asking? We need to rewrite the given equation, which is in exponential form, into logarithmic form. Watch out! Remember the relationship between exponential and logarithmic forms: If $b^x = a$ , then $\log_b a = x$ .
Don't mix up the base and the exponent!

STEP 2

1. Identify the components of the exponential equation.
2. Rewrite the equation in logarithmic form.

STEP 3

Alright, let's break down this exponential equation!
We have $\frac{1}{256} = 4^{-4}$ .
Think of it like this: we have a base raised to an exponent which equals a result.

STEP 4

In our equation, the base is $4$ , the exponent is $-4$ , and the result is $\frac{1}{256}$ .
It's like saying, "4 raised to the power of -4 gives us 1/256."

STEP 5

Remember the magical connection between exponential and logarithmic forms: if $b^x = a$ , then $\log_b a = x$ .
This tells us how to swap between the two forms.

STEP 6

Let's apply this to our equation.
We identified that $b=4$ , $x=-4$ , and $a=\frac{1}{256}$ .
So, plugging these values into the logarithmic form, we get $\log_4 \frac{1}{256} = -4$ .
Boom!

STEP 7

The logarithmic form of $\frac{1}{256} = 4^{-4}$ is $\log_4 \frac{1}{256} = -4$ .

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QuestionWrite in logarithmic form. $\frac{1}{256} = 4^{-4}$ The logarithmic form is $\boxed{}$ . (Use integers or fractions for any numbers in the expression.)

Studdy Solution

STEP 1

What is this asking? We need to rewrite the given equation, which is in exponential form, into logarithmic form. Watch out! Remember the relationship between exponential and logarithmic forms: If $b^x = a$ , then $\log_b a = x$ .
Don't mix up the base and the exponent!

STEP 2

1. Identify the components of the exponential equation.
2. Rewrite the equation in logarithmic form.

STEP 3

Alright, let's break down this exponential equation!
We have $\frac{1}{256} = 4^{-4}$ .
Think of it like this: we have a base raised to an exponent which equals a result.

STEP 4

In our equation, the base is $4$ , the exponent is $-4$ , and the result is $\frac{1}{256}$ .
It's like saying, "4 raised to the power of -4 gives us 1/256."

STEP 5

Remember the magical connection between exponential and logarithmic forms: if $b^x = a$ , then $\log_b a = x$ .
This tells us how to swap between the two forms.

STEP 6

Let's apply this to our equation.
We identified that $b=4$ , $x=-4$ , and $a=\frac{1}{256}$ .
So, plugging these values into the logarithmic form, we get $\log_4 \frac{1}{256} = -4$ .
Boom!

STEP 7

The logarithmic form of $\frac{1}{256} = 4^{-4}$ is $\log_4 \frac{1}{256} = -4$ .

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QuestionWrite in logarithmic form. 1256=4−4\frac{1}{256} = 4^{-4}2561​=4−4 The logarithmic form is \boxed{}​. (Use integers or fractions for any numbers in the expression.)

Studdy Solution

STEP 1

What is this asking? We need to rewrite the given equation, which is in exponential form, into logarithmic form. Watch out! Remember the relationship between exponential and logarithmic forms: If bx=ab^x = abx=a, then log⁡ba=x\log_b a = xlogb​a=x.Don't mix up the base and the exponent!

STEP 2

1. Identify the components of the exponential equation.2. Rewrite the equation in logarithmic form.

STEP 3

Alright, let's break down this exponential equation!We have 1256=4−4\frac{1}{256} = 4^{-4}2561​=4−4.Think of it like this: we have a **base** raised to an **exponent** which equals a **result**.

STEP 4

In our equation, the **base** is 444, the **exponent** is −4-4−4, and the **result** is 1256\frac{1}{256}2561​.It's like saying, "4 raised to the power of -4 gives us 1/256."

STEP 5

Remember the magical connection between exponential and logarithmic forms: if bx=ab^x = abx=a, then log⁡ba=x\log_b a = xlogb​a=x.This tells us how to swap between the two forms.

STEP 6

Let's apply this to our equation.We identified that b=4b=4b=4, x=−4x=-4x=−4, and a=1256a=\frac{1}{256}a=2561​.So, plugging these values into the logarithmic form, we get log⁡41256=−4\log_4 \frac{1}{256} = -4log4​2561​=−4.Boom!

STEP 7

The logarithmic form of 1256=4−4\frac{1}{256} = 4^{-4}2561​=4−4 is log⁡41256=−4\log_4 \frac{1}{256} = -4log4​2561​=−4.

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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 in logarithmic form. $\frac{1}{256} = 4^{-4}$ The logarithmic form is $\boxed{}$ . (Use integers or fractions for any numbers in the expression.)

What is this asking? We need to rewrite the given equation, which is in exponential form, into logarithmic form. Watch out! Remember the relationship between exponential and logarithmic forms: If $b^x = a$ , then $\log_b a = x$ .
Don't mix up the base and the exponent!

1. Identify the components of the exponential equation.
2. Rewrite the equation in logarithmic form.

Alright, let's break down this exponential equation!
We have $\frac{1}{256} = 4^{-4}$ .
Think of it like this: we have a base raised to an exponent which equals a result.

In our equation, the base is $4$ , the exponent is $-4$ , and the result is $\frac{1}{256}$ .
It's like saying, "4 raised to the power of -4 gives us 1/256."

Remember the magical connection between exponential and logarithmic forms: if $b^x = a$ , then $\log_b a = x$ .
This tells us how to swap between the two forms.

Let's apply this to our equation.
We identified that $b=4$ , $x=-4$ , and $a=\frac{1}{256}$ .
So, plugging these values into the logarithmic form, we get $\log_4 \frac{1}{256} = -4$ .
Boom!

The logarithmic form of $\frac{1}{256} = 4^{-4}$ is $\log_4 \frac{1}{256} = -4$ .