Answer:
[tex]x=e^3+4[/tex] (exact)
x = 24.0855 (rounded)
Step-by-step explanation:
We need to remember 3 rules:
1. ln means log_e (ln is log base e)
2. [tex]a^b=x\\SameAS\\log_ax=b[/tex]
3. [tex]aLogx=Logx^a[/tex]
Now we can write the equation as:
[tex]3Ln(x-4)=9\\3Log_e(x-4)=9\\Log_e(x-4)^3=9[/tex]
Now, we can convert it to exponential and solve:
[tex]Log_e(x-4)^3=9\\(x-4)^3=e^9\\\sqrt[3]{(x-4)^3}=\sqrt[3]{e^9} \\ x-4=e^3\\x=e^3+4[/tex]
This is the exact value of x, in 4 decimal places (by using calculator), it would be
x = 24.0855
