Answer:
first option
Step-by-step explanation:
Using the rules of logarithms
log x - log y = log ([tex]\frac{x}{y}[/tex] )
log[tex]x^{n}[/tex] ⇔ n log x
ln e = 1
Given
4 + 5[tex]e^{x+2}[/tex] = 11 ( subtract 4 from both sides )
5[tex]e^{x+2}[/tex] = 7 ( divide both sides by 5 )
[tex]e^{x+2}[/tex] = [tex]\frac{7}{5}[/tex] ( take ln of both sides )
ln [tex]e^{x+2}[/tex] = ln ([tex]\frac{7}{5}[/tex] )
(x + 2) lne = ln ([tex]\frac{7}{5}[/tex] )
x + 2 = ln ([tex]\frac{7}{5}[/tex] ) ( subtract 2 from both sides )
x = ln([tex]\frac{7}{5}[/tex] ) - 2
