Determine the value of the unknown in each of the following

Determine the value of the unknown in each of the following equations. If no possible value of x makes the statement true write DNE.

a) ln(5x)=2.4

b) ln(srt(x+2))=6

c) logbase3(x-8)=4

Please provide an explanation to assist with understanding.

a) ln(5x) = 2.4

use the log property : lna = b ---> a = e^b

So, 5x = e^2.4

x = (e^2.4)/5 = 2.204

b) ln(sqrt(x+2)) = 6

sqrt(x+2) = e^6

taking square on both sides:

x+2= e^12

x = e^12 - 2 = 162752.79

c) log3(x -8) = 4

x- 8 = 3^4

x -8 = 81

x = 89