Alg 2
posted by Yolie .
Solve the equation. Check for extraneous solutions.
10 ln 100x  3 = 117
Thank you in advanced

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
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