yasusar0

2022-07-23

Solve for two variables, two equations with exponents
Solve for both k and x, where $5=k\left(300{\right)}^{x}$ and $80=k\left(600{\right)}^{x}$

Expert

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

Ismael Molina

Expert

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

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