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if 2 to the power x+y=10,2 to the power y+z=20, 2 to the power z+x=30 , then find the value of 2 to the power x
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if 2 to the power x+y=10,2 to the power y+z=20, 2 to the power z+x=30 ...
**Solution:**
To find the value of 2 to the power x, we need to solve the given equations step by step.
Given equations:
1. 2^(xy) = 10
2. 2^(yz) = 20
3. 2^(zx) = 30
To solve these equations, we can take the logarithm of both sides:
1. xy = log2(10)
2. yz = log2(20)
3. zx = log2(30)
Now, let's solve equation 1 for y:
xy = log2(10)
y = log2(10) / x
Substitute this value of y in equation 2:
(log2(10) / x) * z = log2(20)
z = (log2(20) * x) / log2(10)
Similarly, substitute the values of y and z in equation 3:
(log2(30) * (log2(10) / x)) * x = log2(30)
(log2(30) * log2(10)) = x^2
x = sqrt(log2(30) * log2(10))
Now, to find the value of 2^(x), we can substitute the value of x in the equation:
2^(sqrt(log2(30) * log2(10)))
Therefore, the value of 2^(x) is given by the above expression.
Note: The calculation of the exact value of 2^(x) depends on the values of log2(10), log2(20), and log2(30), which can be approximated using a calculator.
To find the value of 2 to the power x, we need to solve the given equations step by step.
Given equations:
1. 2^(xy) = 10
2. 2^(yz) = 20
3. 2^(zx) = 30
To solve these equations, we can take the logarithm of both sides:
1. xy = log2(10)
2. yz = log2(20)
3. zx = log2(30)
Now, let's solve equation 1 for y:
xy = log2(10)
y = log2(10) / x
Substitute this value of y in equation 2:
(log2(10) / x) * z = log2(20)
z = (log2(20) * x) / log2(10)
Similarly, substitute the values of y and z in equation 3:
(log2(30) * (log2(10) / x)) * x = log2(30)
(log2(30) * log2(10)) = x^2
x = sqrt(log2(30) * log2(10))
Now, to find the value of 2^(x), we can substitute the value of x in the equation:
2^(sqrt(log2(30) * log2(10)))
Therefore, the value of 2^(x) is given by the above expression.
Note: The calculation of the exact value of 2^(x) depends on the values of log2(10), log2(20), and log2(30), which can be approximated using a calculator.
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if 2 to the power x+y=10,2 to the power y+z=20, 2 to the power z+x=30 ...
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