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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.
Community Answer
if 2 to the power x+y=10,2 to the power y+z=20, 2 to the power z+x=30 ...
Root under 15
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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 Related: Position Vector - Vector Algebra, Math, Class 12?
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