Answer:
x =60.50 ( nearest hundredth).
Step-by-step explanation:
Given : ln(x+6) - ln9 =2
To find : what is the solution up to nearest hundredth.
Solution : We have given that ln(x+6) - ln9=2
By the logarithm quotient rule ln (a+b) -lnc =[tex]ln\frac{a+b}{c}[/tex].
[tex]ln(x+6) -ln9[/tex] = [tex]ln\frac{x+6}{9}[/tex].
[tex]ln\frac{x+6}{9}[/tex] = 2
Taking exponent both side :
[tex]e(ln\frac{x+6}{9})[/tex] = [tex]e^{2}[/tex].
[tex]\frac{x+6}{9}[/tex] = 7.38
On multiplying both side by 9
(x+6) = 9 * 7.38
x + 6 = 66.42
On subtracting by 6
x = 66.42 - 6
x = 60.42
x =60.50 ( nearest hundredth.)
Therefore, x =60.50 ( nearest hundredth).
