User:Cronholm144/HW

$$\left ( \frac{1}{5} \right )^m \left ( \frac{1}{4} \right )^{18}=\left ( \frac{1}{2 \cdot 10^{35}} \right )$$

$$ {(5^{-1})}^{m} {(4^{-1})}^{18} = 2^{-1} \cdot 10^{-35} $$

$$ {5}^{-m} {4}^{-18} = 2^{-1} \cdot 10^{-35} $$

$$ {5}^{-m} {2}^{-36} = 2^{-1} \cdot 10^{-35} $$

$$ {5}^{-m} {2}^{-35} = 5^{-35} \cdot 2^{-35} $$

$$ {5}^{-m} = 5^{-35} \, $$

$$ m=35 \, $$

$$ {2}^{x} - {2}^{x-2} = 3 \cdot 2^{13} $$

$$ {2}^{x} - {2}^{x} \cdot {2}^{-2} = 3 \cdot 2^{13} $$

$$ {2}^{x} - \frac{1}{4}{2}^{x} = 3 \cdot 2^{13} $$

$$\frac{3}{4}{2}^{x} = 3 \cdot 2^{13} $$

$${2}^{x} = 4 \cdot 2^{13} $$

$${2}^{x} = 2^2 \cdot 2^{13} $$

$${2}^{x} = 2^{15} \,$$

$$ x = 15 \,$$