Solve for two variables, two equations with exponents

Question

Solve for both k and x, where $5=k(300)^x$ and $80=k(600)^x$

Answer 1

$\dfrac{5}{80}=(\dfrac{300}{600})^x$. Can you proceed from here?

Answer 2

Since $$k=\frac{5}{300^x}=\frac{80}{600^x},$$ we have $$5\cdot 300^x\cdot 2^x=80\cdot 300^x\Rightarrow 2^x=\frac{80}{5}=16=2^4.$$

Answer 3

Dividing the second equation by the first gives:

$$\frac {80}5 = \left(\frac {600}{300} \right)^x\\ 16=2^x\\ x=4$$

Substitute back to get $k$.