QuestionCalculate $\log_2{128}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the logarithm of128 to the base. . We know that the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number.

STEP 2

We can write the problem in logarithmic form. In general, if we have a logarithm of a number $n$ to the base $b$ , it can be written as $\log_b n$

STEP 3

For our problem, we can write it as $\log2128$

STEP 4

We need to find the exponent to which2 must be raised to get128. In other words, we need to solve the equation $2^x =128$

STEP 5

We can start by writing128 as a power of2. We know that $2^7 =128$ .

STEP 6

So, we can rewrite the equation as2^x =2^

STEP 7

Since the bases are equal, the exponents must also be equal. So, we can equate the exponents to solve for $x$ $x =7$ So, the logarithm of128 to the base2 is7.

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QuestionCalculate $\log_2{128}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the logarithm of128 to the base. . We know that the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number.

STEP 2

We can write the problem in logarithmic form. In general, if we have a logarithm of a number $n$ to the base $b$ , it can be written as $\log_b n$

STEP 3

For our problem, we can write it as $\log2128$

STEP 4

We need to find the exponent to which2 must be raised to get128. In other words, we need to solve the equation $2^x =128$

STEP 5

We can start by writing128 as a power of2. We know that $2^7 =128$ .

STEP 6

So, we can rewrite the equation as2^x =2^

STEP 7

Since the bases are equal, the exponents must also be equal. So, we can equate the exponents to solve for $x$ $x =7$ So, the logarithm of128 to the base2 is7.

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QuestionCalculate log⁡2128\log_2{128}log2​128.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the logarithm of128 to the base. . We know that the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number.

STEP 2

We can write the problem in logarithmic form. In general, if we have a logarithm of a number nnn to the base bbb, it can be written aslog⁡bn\log_b nlogb​n

STEP 3

For our problem, we can write it aslog⁡2128\log2128log2128

STEP 4

We need to find the exponent to which2 must be raised to get128. In other words, we need to solve the equation2x=1282^x =1282x=128

STEP 5

We can start by writing128 as a power of2. We know that 27=1282^7 =12827=128.

STEP 6

So, we can rewrite the equation as2^x =2^

STEP 7

Since the bases are equal, the exponents must also be equal. So, we can equate the exponents to solve for xxxx=7x =7x=7So, the logarithm of128 to the base2 is7.

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Start learning now

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

QuestionCalculate $\log_2{128}$ .

We can write the problem in logarithmic form. In general, if we have a logarithm of a number $n$ to the base $b$ , it can be written as $\log_b n$

For our problem, we can write it as $\log2128$

We need to find the exponent to which2 must be raised to get128. In other words, we need to solve the equation $2^x =128$

We can start by writing128 as a power of2. We know that $2^7 =128$ .

Since the bases are equal, the exponents must also be equal. So, we can equate the exponents to solve for $x$ $x =7$ So, the logarithm of128 to the base2 is7.