Tìm x biết: 2^x = (-1 + √1075)/(-6); 2^x = (-1 - √1075)/(-6)

To solve these equations, we can use logarithms. Taking the logarithm of both sides of each equation will allow us to isolate the exponent, x.

1) Taking the logarithm of both sides of the equation 2^x = (-1 + √1075) / (-6), we get:
log(2^x) = log((-1 + √1075) / (-6))

Using the property of logarithms that states log(a^b) = b * log(a), we can rewrite the equation as:
x * log(2) = log((-1 + √1075) / (-6))

Now, we can solve for x by dividing both sides of the equation by log(2):
x = log((-1 + √1075) / (-6)) / log(2)

2) Similarly, taking the logarithm of both sides of the equation 2^x = (-1 - √1075) / (-6), we get:
log(2^x) = log((-1 - √1075) / (-6))

Using the property of logarithms, we can rewrite the equation as:
x * log(2) = log((-1 - √1075) / (-6))

Solving for x by dividing both sides of the equation by log(2), we get:
x = log((-1 - √1075) / (-6)) / log(2)