SOLUTION: Solve the logarithmic equation algebraically.Approximate the result to three decimal places. log(4x)-log(14+the square root of x)=2

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
**
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

RELATED QUESTIONS
Solve the logarithmic equation algebraically. Approximate the result to three decimal... (answered by LinnW)

Please help me solve this question: Solve the logarithmic equation algebraically.... (answered by Alan3354)

Please help me solve this equation: Solve the logarithmic equation algebraically.... (answered by robertb)

ln(x) + ln(x � 5) = 4 Solve the logarithmic equation algebraically Approximate the... (answered by jsmallt9)

Solve the exponential equation algebraically. Approximate the result to three decimal... (answered by checkley77)

Solve the logarithmic equation algebraically. Round to three decimal places. log... (answered by CharlesG2)

Solve the logarithmic equation algebraically. Approximate the result to three decimal... (answered by robertb)

Solve the logarithmic equation algebraically. Approximate the result to three decimal... (answered by lwsshak3)

Solve the exponential equation algebraically. Round the result to three decimal places. (answered by tommyt3rd)