Question

necesito resolver este ejercico de matematicas 5 elevado 2x-1=3 elevado 4x+2

Answer 1

$\ln \left(5^{2x-1}\right)=\ln \left(3^{4x+2}\right)$

$\left(2x-1\right)\ln \left(5\right)=\left(4x+2\right)\ln \left(3\right)$

$\left(2x-1\right)\ln \left(5\right) =\ln \left(5\right)\cdot \:2x+\ln \left(5\right)\left(-1\right)$
$=\ln \left(5\right)\cdot \:2x-\ln \left(5\right)\cdot \:1$

$2x\ln \left(5\right)-\ln \left(5\right)=4x\ln \left(3\right)+2\ln \left(3\right)$

$2x\ln \left(5\right)-\ln \left(5\right)+\ln \left(5\right)=4x\ln \left(3\right)+2\ln \left(3\right)+\ln \left(5\right)$

$2x\ln \left(5\right)=4x\ln \left(3\right)+\ln \left(45\right)$

$2x\ln \left(5\right)-4x\ln \left(3\right)=4x\ln \left(3\right)+\ln \left(45\right)-4x\ln \left(3\right)$

$2x\ln \left(5\right)-4x\ln \left(3\right)=4x\ln \left(3\right)+\ln \left(45\right)-4x\ln \left(3\right)$$2x\ln \left(5\right)-4x\ln \left(3\right)$
$=2x\left(\ln \left(5\right)-2\ln \left(3\right)\right)$$=2x\ln \left(\frac{5}{9}\right)$

$2x\ln \left(\frac{5}{9}\right)=\ln \left(45\right)$$\frac{2x\ln \left(\frac{5}{9}\right)}{2\ln \left(\frac{5}{9}\right)}=\frac{\ln \left(45\right)}{2\ln \left(\frac{5}{9}\right)}$

$x=\frac{\ln \left(45\right)}{2\ln \left(\frac{5}{9}\right)}$