Tenemos la ecuación
$$\frac{\log{\left(5 x - 7 \right)}}{\log{\left(2 \right)}} - \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(21 \right)}}{\log{\left(2 \right)}}$$
$$\frac{\log{\left(5 x - 7 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(21 \right)}}{\log{\left(2 \right)}}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =1/log(2)
$$\log{\left(5 x - 7 \right)} = \left(\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(21 \right)}}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$5 x - 7 = e^{\frac{\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(21 \right)}}{\log{\left(2 \right)}}}{\frac{1}{\log{\left(2 \right)}}}}$$
simplificamos
$$5 x - 7 = e^{\left(\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(21 \right)}}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}}$$
$$5 x = 7 + e^{\left(\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(21 \right)}}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}}$$
$$x = \frac{7}{5} + \frac{e^{\left(\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(21 \right)}}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}}}{5}$$