Respuesta :
Question: Solve the equation:
[tex]\ln (7x-4)=\text{ ln(2x+11)}[/tex]Solution:
applying the laws of logarithms (applying the inverse function of the logarithm function) we get:
[tex]e^{\ln (7x-4)}=e^{\text{ ln(2x+11)}}[/tex]this is equivalent to:
[tex]7x-4=\text{ 2x+11}[/tex]putting similar terms together we get:
[tex]7x-2x=11+4[/tex]this is equivalent to:
[tex]5x\text{ = 15}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{15}{5}\text{ = 3}[/tex]then, we can conclude that the solution of the equation is:
[tex]x\text{ = 3}[/tex]
