Logs and natural logs question? plz help me out!?

Question

Solve for x, where x is a real number. Show the work that leads to your solution.

1) log x + log (x-3) = 1

2) e^3k = 5

3) ln y = 2t - 3

Answer 1

1 .

log x + log (x+3) =1 or log {x.(x+3)} = 1

or x(x+3) = 10^1 or x^2 +3x - 10 =0

or x^2 + 5x -2x -10 = 0 or x(x+5)  -2(x+5) =0

or (x-2)(x+5) =0 or x =2 or -5.

Eqn ax^2 + bx +c =0 can also be solved by

x = {-b +/- sqrt(b^2 -4ac)}/ 2a

2.

e^3k = 5

or ln 5 = 3k  (log base e)

or k = (ln 5)/3

3

ln y = 2t -3

e^(2t -3) =y

Answer 2

log(a) + log(b) = log(a*b)

log(x) + log(x-3) = 1

log(x(x-3)) = 1

log(x² - 3x) = 1

10^1 = x² - 3x

0 = x² - 3x - 10

0 = (x-5)(x+2)

x = 5 (cannot log a negative number so x= -2 isn't valid)

e^(3k) = 5

ln[ e^(3k) ] = ln(5)

3k = ln(5)

k = ln(5)/3

ln(y) = 2t - 3

e^(lny) = e^(2t-3)

y = e^(2t-3)

Neither of your latter 2 questions have x in them, so I don't know what to solve for really...

♠