Question 685036: Solve the logarithmic equation algebraically.Approximate the result to three decimal places.
log(4x)-log(14+the square root of x)=2 Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Solve the logarithmic equation algebraically.Approximate the result to three decimal places.
log(4x)-log(14+the square root of x)=2
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log(4x)-log(14+√x)=2
log[4x/(14+x^(1/2))=2
convert to exponential form
10^2=4x/(14+x^(1/2))=100
4x=1400+100x^(1/2)
4x-1400-100x^(1/2)=0
let u=x^(1/2)
u^2=x
4u^2-100u-1400=0
u^2-25u-350=0
(u-35)(u+10)
u=35=√x
x=35^2=1225
or
u=-10=√x
x=(-10)^2=100
ans:
x=1225
or
x=100
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