Question 458330: Solve: log base7(2x+9) = log base7x+log base7(x+10)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Solve: log base7(2x+9) = log base7x+log base7(x+10)
..
log7(2x+9)=log7(x)+log7(x+10)
log7(2x+9)-(log7(x)+log7(x+10)=0
place under single log
log7[(2x+9)/(x)(x+10)=0
log7[(2x+9)/(x^2+10x)]=0
convert to exponential form: (base(7) raised to log of number(0)=number[(2x+9)/(x^2+10x)]
7^0=[(2x+9)/(x^2+10x)]=1
2x+9=x^2+10x
x^2+8x-9=0
(x+9)(x-1)=0
x=-9 (reject, x>0)
or
x=1 (ans)
|
|
|
