Question

what is the true solution to the equation?
$2\ln e^{\ln 2x} - \ln e^{\ln 10x} = \ln 30$
$x = 300$
$x = 150$
$x = 30$
$x = 75$

Explanation:

Step1: Aplicar propiedad $\ln e^a = a$

$2\ln 2x - \ln 10x = \ln 30$

Step2: Aplicar propiedad $a\ln b = \ln b^a$

$\ln (2x)^2 - \ln 10x = \ln 30$

Step3: Aplicar propiedad $\ln a - \ln b = \ln \frac{a}{b}$

$\ln \frac{(2x)^2}{10x} = \ln 30$

Step4: Igualar argumentos de logaritmos

$\frac{4x^2}{10x} = 30$

Step5: Simplificar y resolver para $x$

$\frac{2x}{5} = 30 \implies 2x = 150 \implies x = 75$

Answer:

$x = 75$