SOLUTION: I can not figure out for the life of me how to do this. I have tried so many times, please, HELP. Solve: 3log(5x)+4log(2x)=3 log(125x^3)+log(16x^4)=3 Have I done it right s

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I can not figure out for the life of me how to do this. I have tried so many times, please, HELP. Solve: 3log(5x)+4log(2x)=3 log(125x^3)+log(16x^4)=3 Have I done it right s      Log On


   

Question 39666: I can not figure out for the life of me how to do this. I have tried so many times, please, HELP.
Solve:
3log(5x)+4log(2x)=3
log(125x^3)+log(16x^4)=3
Have I done it right so far? For some reason it seems wrong.Please help me!!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct as far as you have gone.
log%28125x%5E3%29%2Blog%2816x%5E4%29+=+3 Now apply the "product rule" for logarthms:log%28M%29%2Blog%28N%29+=+logMN
log%28%28125x%5E3%29%2816x%5E4%29%29+=+3 Simplify.
log%282000x%5E7%29+=+3 Convert to exponential form.
10%5E3+=+2000x%5E7 Divide both sides by 2000.
1%2F2+=+x%5E7
x+=+0.9057Approximately.