$\frac{256}{2^S}=64$
How would you solve for S?
$\frac{256}{2^S}=64$
How would you solve for S?
Well, think of $\frac{256}{2{^s}}$ as $256$ divided by $2^{s}$. then think of what multiplied by $64$ is equal to $256$. Now, $2$ to what power(s) will equal this number?
Hint: $256=2^8$, $64=2^6$, and remember the rule $2^x/2^y = 2^{x-y}$.
Here is one solution to your problem. $\frac{256}{2^s}=64$ $256 = 64\cdot2^s$ Since $64 = 2^6$ and $256 = 2^8$ the equation becomes: $2^8 = 2^6\cdot 2^s$ Simplify using the law: $a^b \cdot a^c = a^{b+c}$. $2^8 = 2^{6+s}$ Equate the exponents (this is only allowed when the bases are equal). $8 = 6+s$ $2 = s$ ...or equivalently: $s = 2$
I would start by dividing by $64$ and multiplying by $2^S$ to give $2^S=\frac {256}{64}=4$. Converting $256$ and $64$ to powers of $2$ seems unnecessary complication to me.
FURTHER HINT: $\mathrm{log}_2(2^{x}) = x$