SOLUTION: Please help and show all work step by step. I have tried this and the answer I came up with was 11 but it was wrong. Find the largest value of x that satisfies: log_5(x^2)-lo

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help and show all work step by step. I have tried this and the answer I came up with was 11 but it was wrong. Find the largest value of x that satisfies: log_5(x^2)-lo      Log On


   

Question 998780: Please help and show all work step by step. I have tried this and the answer I came up with was 11 but it was wrong.
Find the largest value of x that satisfies:
log_5(x^2)-log_5(x+4)=7
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Use better notation. Is base 5?
Another one very similar was solved a short time ago today.

Pure text before rendering tags, log(5,(x^2))-log(5,(x+4))=7

log%285%2C%28x%5E2%29%29-log%285%2C%28x%2B4%29%29=7
log%285%2C%28x%5E2%2F%28x%2B4%29%29%29=7
Put into exponential form.
5%5E7=x%5E2%2F%28x%2B4%29

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http://www.algebra.com/algebra/homework/Exponential-and-logarithmic-functions/Exponential-and-logarithmic-functions.faq.question.998769.html

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%285%2Cx%5E2%29-log%285%2C%28x%2B4%29%29=7

log%285%2Cx%5E2%2F%28x%2B4%29%29=7......change the base

log%28x%5E2%2F%28x%2B4%29%29%2Flog%285%29=7

log%28x%5E2%2F%28x%2B4%29%29=7log%285%29

log%28x%5E2%2F%28x%2B4%29%29=log%285%5E7%29....if log same, than we have

x%5E2%2F%28x%2B4%29=5%5E7

x%5E2%2F%28x%2B4%29=78125

x%5E2=78125%28x%2B4%29

x%5E2=78125x%2B312500

x%5E2-78125x-312500=0.....use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



x+=+%2878125+%2B-+sqrt%28+6103515625%2B1250000+%29%29%2F2+

x+=+%2878125+%2B-+sqrt%28+6104765625+%29%29%2F2+

x+=+%2878125+%2B-7625sqrt%28105%29%29%2F2+

solutions:

x+=+%2878125+%2B7625+sqrt%28105%29%29%2F2+=>x+=+78125%2F2+%2B7625sqrt%28105%29%29%2F2+

x+=+%2878125+-7625+sqrt%28105%29%29%2F2+=>x+=+78125%2F2+-7625sqrt%28105%29%29%2F2+

the largest value of x that satisfies is:
x+=+%2878125+%2B7625+sqrt%28105%29%29%2F2+=>x+=+78125%2F2+%2B7625sqrt%28105%29%29%2F2+
approximately x=78128.9998