Question

Solve for x.

3ln(x-4)=9​

Answer 1

`x=e^3+4` (exact)

x = 24.0855 (rounded)

Explanation:

We need to remember 3 rules:

1. ln means log_e (ln is log base e)

2.
`a^b=x\\SameAS\\log_ax=b`

3.
`aLogx=Logx^a`

Now we can write the equation as:

`3Ln(x-4)=9\\3Log_e(x-4)=9\\Log_e(x-4)^3=9`

Now, we can convert it to exponential and solve:

`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`

This is the exact value of x, in 4 decimal places (by using calculator), it would be

x = 24.0855