SOLUTION: Please help in solving the equation for x : ln⁡〖5x^2 〗- ln⁡x = 3 a) 0.22 b) 0.60 c) 1.59 d) 4.02 Would very much appreciate if workings can be sho

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help in solving the equation for x : ln⁡〖5x^2 〗- ln⁡x = 3 a) 0.22 b) 0.60 c) 1.59 d) 4.02 Would very much appreciate if workings can be sho      Log On


   

Question 991937: Please help in solving the equation for x : ln⁡〖5x^2 〗- ln⁡x = 3
a) 0.22
b) 0.60
c) 1.59
d) 4.02
Would very much appreciate if workings can be shown, thank you.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
answer is d (4.02).

here's why:

ln(5x^2) - ln(x) = 3

since ln(a) - ln(b) = ln(a/b), you get:

ln(5x^2) - ln(x) = 3 becomes:

ln(5x^2/x) = 3

simplify to get:

ln(5x) = 3

this is true if and only if e^3 = 5x

solve for x to get:

x = e^3 / 5

evaluate to get:

x = 4.017107385 which rounds to 4.02.

confirm your solution is correct by replacing x with 4.017107385 in your original equation and you will see that the equation is true.