Answer:
x=0.996
Step-by-step explanation:
[tex]3e^{2x} +5=27[/tex]
To take natural log ln , we need to get e^2x alone
Subtract 5 on both sides
[tex]3e^{2x}=22[/tex]
Now we divide both sides by 3
[tex]e^{2x}=\frac{22}{3}[/tex]
Now we take 'ln' on both sides
[tex]ln(e^{2x})=ln(\frac{22}{3})[/tex]
As per log property we can move exponent 2x before ln
[tex](2x)ln(e)=ln(\frac{22}{3})[/tex]
The value of ln(e) = 1
[tex]2x=ln(\frac{22}{3})[/tex]
Divide both sides by 2
[tex]x=\frac{ln(\frac{22}{3})}{2}[/tex]
x= 0.996215082
Round to nearest thousandth
x=0.996
