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



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


{{{log(2, x) + log(2, (x + 2)) = log(2, (6x + 1))}}}


{{{log(2, x(x + 2)) = log(2, (6x + 1))}}}


x(x + 2) = 6x + 1


{{{x^2 + 2x = 6x + 1)))


{{{x^2 + 2x - 6x - 1 = 0}}}


{{{x^2 - 4x - 1 = 0}}}


Solving using the quadratic formula, x = {{{highlight_green(4.236067977)}}}




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


{{{log (x) - log ((x - 1)) = 2}}}


{{{log (x/(x - 1)) = 2}}}


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


{{{x/(x - 1) = 10^2}}}


{{{x/(x - 1) = 100}}}


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


100x - 100 = x


100x - x = 100


99x = 100


{{{highlight_green(x = 100/99)}}}, or {{{highlight_green(1&1/99)}}}


You can do the check on each!!


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