Question

Which equation can be one of the steps in the process of finding the solution to e2x = 100? a.x = 1/ln e b.x = ln e/ln 100 c.x = ln 100/(2ln e)

Answer 1

`\bf \textit{Logarithm Cancellation Rules}\\\\ \boxed{log_a a^x\implies x}\qquad \qquad a^(log_ax)=x\\\\ -------------------------------\\\\ %e2x = 100 e^(2x)=100\implies log_e(e^(2x))=log_e(100)\implies 2x\cdot log_e(e)=log_e(100) \\\\\\ x=\cfrac{log_e(100)}{2log_e(e)}\implies \boxed{x=\cfrac{ln(100)}{2ln(e)}}\implies x=\cfrac{log_e(100)}{2log_e(e)} \\\\\\ x=\cfrac{log_e(10^2)}{2log_e(e)}\implies x=\cfrac{2log_e(10)}{2log_e(e)} \\\\\\ x=\cfrac{2log_e(10)}{2(1)}\implies x=ln(10)`