SOLUTION: Can anyone help? Question: prove that the value of x that satisfies 2log2x + log2(x-1) = 1+log2(35x + 100) is a solution of the equation x^3 - x^2 - 70x - 200 = 0

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can anyone help? Question: prove that the value of x that satisfies 2log2x + log2(x-1) = 1+log2(35x + 100) is a solution of the equation x^3 - x^2 - 70x - 200 = 0      Log On


   

Question 1074217: Can anyone help?
Question: prove that the value of x that satisfies 2log2x + log2(x-1) = 1+log2(35x + 100) is a solution of the equation x^3 - x^2 - 70x - 200 = 0
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

2log%282%2C%28x%29%29+%2B+log%282%2C%28x-1%29%29+=+1%2Blog%282%2C%2835x+%2B+100%29%29

Use the rule of logarithms on the first term that allows
a coefficient of a logarithm to be moved to the exponent
of the expression which the logarithm is of.

log%282%2C%28x%5E2%29%29+%2B+log%282%2C%28x-1%29%29+=+1%2Blog%282%2C%2835x+%2B+100%29%29

Since log2(2) = 1 we can replace the 1 on the
right by that:



Use the rule of logarithms that allows a sum of logarithms
to be written as the logarithm of the product of the 
expressions which the logarithms are of.

log%282%2C%28x%5E2%28x-1%29%29%29+=+log%282%2C%282%5E%22%22%2835x+%2B+100%29%29%29

Use the rule of logarithms  that if log%28B%2CA%29=log%28B%2CC%29, then A=C

x%5E2%28x-1%29+=+2%2835x+%2B+100%29

x%5E3-x%5E2+=+70x+%2B+200

x%5E3-x%5E2+-+70x+-+200=0

Edwin