Solved on Jan 23, 2024

Find the two integers between which $x$ lies when $2^{x} = 50$ .

STEP 1

Assumptions
1. We are given the equation $2^{x} = 50$ .
2. We need to find two consecutive integers between which $x$ lies.
3. We will use the properties of exponents and logarithms to solve the problem.

STEP 2

To determine between which two integers $x$ lies, we need to find two powers of 2 that are immediately less than and greater than 50. We will start by listing powers of 2 until we find the two integers that satisfy the condition.

STEP 3

List the powers of 2 that are close to 50:
$2^1 = 2$ $2^2 = 4$ $2^3 = 8$ $2^4 = 16$ $2^5 = 32$ $2^6 = 64$

STEP 4

From the list above, we can see that $2^5 = 32$ and $2^6 = 64$ . Since 32 is less than 50 and 64 is greater than 50, we can conclude that $2^5 < 2^x < 2^6$ .

STEP 5

Now, we can state that $x$ is between the exponents 5 and 6 because $2^5 < 50 < 2^6$ .

STEP 6

Therefore, $x$ lies between the integers 5 and 6.
$x$ lies between the integers 5 and 6.

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Find the two integers between which $x$ lies when $2^{x} = 50$ .

STEP 1

Assumptions
1. We are given the equation $2^{x} = 50$ .
2. We need to find two consecutive integers between which $x$ lies.
3. We will use the properties of exponents and logarithms to solve the problem.

STEP 2

To determine between which two integers $x$ lies, we need to find two powers of 2 that are immediately less than and greater than 50. We will start by listing powers of 2 until we find the two integers that satisfy the condition.

STEP 3

List the powers of 2 that are close to 50:
$2^1 = 2$ $2^2 = 4$ $2^3 = 8$ $2^4 = 16$ $2^5 = 32$ $2^6 = 64$

STEP 4

From the list above, we can see that $2^5 = 32$ and $2^6 = 64$ . Since 32 is less than 50 and 64 is greater than 50, we can conclude that $2^5 < 2^x < 2^6$ .

STEP 5

Now, we can state that $x$ is between the exponents 5 and 6 because $2^5 < 50 < 2^6$ .

STEP 6

Therefore, $x$ lies between the integers 5 and 6.
$x$ lies between the integers 5 and 6.

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Find the two integers between which xxx lies when 2x=502^{x} = 502x=50.

STEP 1

Assumptions1. We are given the equation 2x=502^{x} = 502x=50.2. We need to find two consecutive integers between which xxx lies.3. We will use the properties of exponents and logarithms to solve the problem.

STEP 2

To determine between which two integers xxx lies, we need to find two powers of 2 that are immediately less than and greater than 50. We will start by listing powers of 2 until we find the two integers that satisfy the condition.

STEP 3

List the powers of 2 that are close to 50:21=22^1 = 221=2 22=42^2 = 422=4 23=82^3 = 823=8 24=162^4 = 1624=16 25=322^5 = 3225=32 26=642^6 = 6426=64

STEP 4

From the list above, we can see that 25=322^5 = 3225=32 and 26=642^6 = 6426=64. Since 32 is less than 50 and 64 is greater than 50, we can conclude that 25<2x<262^5 < 2^x < 2^625<2x<26.

STEP 5

Now, we can state that xxx is between the exponents 5 and 6 because 25<50<262^5 < 50 < 2^625<50<26.

STEP 6

Therefore, xxx lies between the integers 5 and 6.xxx lies between the integers 5 and 6.

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Find the two integers between which $x$ lies when $2^{x} = 50$ .

Assumptions
1. We are given the equation $2^{x} = 50$ .
2. We need to find two consecutive integers between which $x$ lies.
3. We will use the properties of exponents and logarithms to solve the problem.

To determine between which two integers $x$ lies, we need to find two powers of 2 that are immediately less than and greater than 50. We will start by listing powers of 2 until we find the two integers that satisfy the condition.

List the powers of 2 that are close to 50:
$2^1 = 2$ $2^2 = 4$ $2^3 = 8$ $2^4 = 16$ $2^5 = 32$ $2^6 = 64$

From the list above, we can see that $2^5 = 32$ and $2^6 = 64$ . Since 32 is less than 50 and 64 is greater than 50, we can conclude that $2^5 < 2^x < 2^6$ .

Now, we can state that $x$ is between the exponents 5 and 6 because $2^5 < 50 < 2^6$ .

Therefore, $x$ lies between the integers 5 and 6.
$x$ lies between the integers 5 and 6.