Question

10^x • 100^2x = 1000^5. Solve for x, step by step.

Answer 1

$\bf 10^x\cdot 10^{2x}=1000^5\qquad \boxed{1000=10^3}\qquad 10^x\cdot 10^{2x}=(10^3)^5 \\\\\\ 10^{x+2x}=10^{3\cdot 5}\implies 10^{3x}=10^{15}\impliedby \begin{array}{llll} \textit{the bases are the same, thus}\\ \textit{exponents must also}\\ \textit{be the same} \end{array} \\\\\\ 3x=15\implies x=\cfrac{15}{3}\implies x=5$