SOLUTION: I am having difficulty solving 2 problems. I would appreciate if someone can help me. Thank you. 1. Solve for x: log base 2 X + log base 2 (x+2)) = log base 2 (6x+1) 2. Solve

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am having difficulty solving 2 problems. I would appreciate if someone can help me. Thank you. 1. Solve for x: log base 2 X + log base 2 (x+2)) = log base 2 (6x+1) 2. Solve      Log On


   

Question 748556: I am having difficulty solving 2 problems. I would appreciate if someone can help me. Thank you.
1. Solve for x: log base 2 X + log base 2 (x+2)) = log base 2 (6x+1)
2. Solve for y in terms of x: log x - log (x-1) = 2
Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

I am having difficulty solving 2 problems. I would appreciate if someone can help me. Thank you.
1. Solve for x: log base 2 X + log base 2 (x+2)) = log base 2 (6x+1)
2. Solve for y in terms of x: log x - log (x-1) = 2


1. Solve for x: log base 2 X + log base 2 (x+2)) = log base 2 (6x+1)

log%282%2C+x%29+%2B+log%282%2C+%28x+%2B+2%29%29+=+log%282%2C+%286x+%2B+1%29%29

log%282%2C+x%28x+%2B+2%29%29+=+log%282%2C+%286x+%2B+1%29%29

x(x + 2) = 6x + 1

x%5E2+%2B+2x+=+6x+%2B+1%29%29%29%0D%0A%0D%0A%0D%0A%7B%7B%7Bx%5E2+%2B+2x+-+6x+-+1+=+0

x%5E2+-+4x+-+1+=+0

Solving using the quadratic formula, x = highlight_green%284.236067977%29



2. Solve for y in terms of x: log x - log (x-1) = 2

log+%28x%29+-+log+%28%28x+-+1%29%29+=+2

log+%28x%2F%28x+-+1%29%29+=+2

As there's no indicated base, we know we're dealing with base 10, so we have:

x%2F%28x+-+1%29+=+10%5E2

x%2F%28x+-+1%29+=+100

100(x - 1) = x -------- Cross-multiplying

100x - 100 = x

100x - x = 100

99x = 100

highlight_green%28x+=+100%2F99%29, or highlight_green%281%261%2F99%29

You can do the check on each!!

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com