# How do you solve 2^(3-x) = 565?

$x = 3 - \frac{\log 565}{\log 2} = - 6.142107057$

#### Explanation:

We start from the given equation

${2}^{3 - x} = 565$

Take the logarithm of both sides

$\log {2}^{3 - x} = \log 565$

$\left(3 - x\right) \cdot \log 2 = \log 565$

$3 - x = \log \frac{565}{\log} 2$

$3 - \log \frac{565}{\log} 2 = x$

and

$x = 3 - \frac{\log 565}{\log 2} = - 6.142107057$

God bless....I hope the explanation is useful