Question

Solve 10e^2x - 5 =23^x for x.

Answer 1

B is the correct option choice !

Answer 2

`10e^(2x)-5=23e^x\qquad\text{subtract}\ 23e^x\ \text{from both sides}\\\\10e^(2x)-23e^x-5=0\\\\10(e^x)^2-23(e^x)-5=0\\\\\text{substitution:}\ e^x=t > 0\\\\10t^2-23t-5=0\\\\10t^2-25t+2t-5=0\\\\5t(2t-5)+1(2t-5)=0\\\\(2t-5)(5t+1)=0\iff2t-5=0\ \vee\ 5t+1=0\\\\2t=5\ \vee\ 5t=-1\\\\t=(5)/(2) > 0\ \vee\ t=-(1)/(5) < 0\\\\\text{therefore}\ e^x=(5)/(2)\to\ln e^x=\ln\left((5)/(2)\right)\\\\\boxed{x=\ln\left((5)/(2)\right)}`