Answer
[tex]x=\frac{e^{4}-6}{4}\approx12.15[/tex]
Explanation
Given:
[tex]\ln(4x+6)=4[/tex]
As it is a natural logarithm, the base for this is Euler's constant, meaning that:
[tex]e^{\ln(a)}=a[/tex]
Thus, applying this to both sides of the equation we get:
[tex]e^{\operatorname{\ln}(4x+6)}=e^4[/tex][tex]4x+6=e^4[/tex]
Solving for x:
[tex]4x=e^4-6[/tex][tex]x=\frac{e^4-6}{4}\approx12.15[/tex]
