Answer:
[tex]x=\frac{e^3}{10}[/tex]
Step-by-step explanation:
We have the equation
[tex]ln5 +ln 2x=3[/tex]
The first step to simplify is to use the following property of logarithms
[tex]lna+lnb=ln(a*b)[/tex], in this case a=5 and b=2x
So the original equation becomes:
[tex]ln(5*2x)=3[/tex]
[tex]ln(10x)=3[/tex]
The inverse operation of the natural logarithm is the exponential [tex]e[/tex]
Thus Using the following property:
[tex]e^{lnk} =k[/tex]
The equation now is:
[tex]e^{ln10x} =e^{3}[/tex]
⇒[tex]10x=e^3[/tex]
thus, x will be:
[tex]x=\frac{e^3}{10}[/tex]
