SOLUTION: How do I find a solution for : Log base of 10 4x - log base of 10 (12 + square root of x) = 2

Question 406920: How do I find a solution for :
Log base of 10 4x - log base of 10 (12 + square root of x) = 2
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Log base of 10 4x - log base of 10 (12 + square root of x) = 2
..
log4x-log(12+sqrt(x)=2
applying division rule,
log(4x/(12+sqrt(x)=2
convert to exponential form (the base raised to the logarithm of the number is equal to the number. In this case the base=10, the logarithm of the number=2, and the number is (4x/(12+sqrt(x))
4x/(12+sqrt(x)=10^2=100
4x=1200+100sqrt(x)
x=300+25sqrt(x)
x-25sqrt(x)-300=0
let u=sqrt(x)
then u^2=x
u^2-25u-300=0
using quadratic formula to solve,
a=1,b=-25,c=-300
u=-(-25)+-sqrt((-25)^2-4(1)(-300))/2(1)
u=(25+-sqrt(1825))/2
u=(25+-42.72)/2
u=33.86
u=-8.86 (reject, in log x, x>0
x=u^2=(33.86)^2=1146.5
..
check:
log4x-log(12+sqrt(x)
log(4*1146.5)-log(12+sqrt(1146.5)
log(4586)-log(45.86)
=3.66-1.66=2=right-hand side

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