SOLUTION: Solve the equation. log(x+5)-logx=3

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Question 1009725: Solve the equation.
log(x+5)-logx=3
Found 3 solutions by addingup, MathLover1, MathTherapy:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
log(x+5)-logx=3
log(1/x)+log(x+5)= 3
log((x+5)/x)= 3 now take exponent on both sides to get rid of log
(x+5)/x= e^3 multiply both sides times x:
x+5= e^3x subtract 5+e^3 from both sides
(1-e^3)x= -5
Divide both sides by 1-e^3:
x= -5/(1-e^3)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

log%28%28x%2B5%29%29-log%28%28x%29%29=3
log%28%28%28x%2B5%29%2Fx%29%29=3....in base 10 will be
log%28%28%28x%2B5%29%2Fx%29%29%2Flog%28%2810%29%29=3
log%28%28%28x%2B5%29%2Fx%29%29=3log%28%2810%29%29
log%28%28%28x%2B5%29%2Fx%29%29=log%28%2810%5E3%29%29...if log same, we have
%28x%2B5%29%2Fx=10%5E3
%28x%2B5%29%2Fx=1000
x%2B5=1000x
5=1000x-x
5=999x
x=5%2F999


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the equation.
log(x+5)-logx=3
log (x + 5) – log x = 3

log+%28%28x+%2B+5%29%29%2Fx+=+3

%28x+%2B+5%29%2Fx+=+10%5E3 ------- Converting to EXPONENTIAL form

%28x+%2B+5%29%2Fx+=+1000

1,000x = x + 5 ----- Cross-multiplying

1,000x – x = 5

999x = 5_______highlight_green%28x+=+5%2F999%29