Question

Resuelva el siguiente
a) 4.9955
b) 2.155
c) 0.155
d) 6.5599

Answer 1

$(2^x)^x = 25 \\ \\ e^{x\ln \left(2^x\right)}=25 \\ \\ \ln \left(e^{x\ln \left(2^x\right)}\right)=\ln \left(25\right) \\ \\ x\ln \left(2^x\right)\ln \left(e\right)=\ln \left(25\right) \\ \\ \textbf{Factorizamos:} \\ \\ x\ln \left(2^x\right)\ln \left(e\right) \\ \\ = 1\cdot \ln \left(2\right)x^2 \\\\ = \ln \left(2\right)x^2 \\ \\ \ln \left(5^2\right) = 2\ln \left(5\right)$

$\textbf{Reescribimos:} \\ \\ \dfrac{\ln \left(2\right)x^2}{\ln \left(2\right)}=\dfrac{2\ln \left(5\right)}{\ln \left(2\right)} \\\\\\ x^2=\dfrac{2\ln \left(5\right)}{\ln \left(2\right)} \\ \\ \textbf{Sacamos raiz cuadrada} \\ \\ x=\sqrt{\dfrac{2\ln \left(5\right)}{\ln \left(2\right)}},\:x=-\sqrt{\dfrac{2\ln \left(5\right)}{\ln \left(2\right)}}$

$\left(\mathrm{Decimal:\quad }x=2.15496\dots ,\:\quad x=-2.15496\dots \right) \\ \\ \textbf{Respuesta correcta: B \ \checkmark}$

¡Espero haberte ayudado, saludos... G.G.H!