Question

Solve the equation. Check for extraneous solutions.

10 ln 100x - 3 = 117

Thank you in advanced

Answer 1

10 log(100 x)-3 = 117

Add 3 to both sides:

10 log(100 x)- 3 = 117 + 3

10 log(100 x) = 120

Divide both sides by 10:

log(100 x) = 12

Cancel logarithms by taking exp of both sides:

100 x = e^12

Divide both sides by 100:

x = e^12/100

Now test that this solution is appropriate by substitution into the original equation:

Check the solution x = e^12/100:

10 log(100 x)- 3 = -3 + 10 log((100 e^12)/100) = 117

So the solution is correct.

Thus, the solution is:

x = e^12/100