In the equation log x + log ( x + 3 ) = 1, x is equal to?
how do you solve this?
2007-04-22 19:34:54 · 5 answers · asked by killz_me08 1 in Science & Mathematics ➔ Mathematics
log x + log ( x + 3 ) = 1
log x( x + 3 ) = 1 ---- Using log(ab) = log a + log b
log x( x + 3 ) = log 10 ---- Using log 10 = 1
x(x+3) = 10
x^2 + 3x -10 = 0
(x+5)(x-2) = 0
x = 2 or x = -5(N.A)
=>answer: x=2
2007-04-22 19:40:07 · answer #1 · answered by QiQi 3 · 0⤊ 1⤋
log(x) + log(x + 3) = 1
log(x(x + 3)) = 1
log(x^2 + 3x) = 1
inverse log both sides
x^2 + 3x = 10^1
x^2 + 3x = 10
x^2 + 3x - 10 = 0
(x + 5)(x - 2) = 0
x = -5 or 2
since you can't do log(-5)
ANS : x = 2
2007-04-23 02:54:50 · answer #2 · answered by Sherman81 6 · 0⤊ 0⤋
log[(2x + 3) ] = 1
2x + 3 = 10 (in base ten logs)
2x = 7
x = 7/2 = 3.5
2007-04-23 02:48:18 · answer #3 · answered by Como 7 · 0⤊ 0⤋
log (x^2 + 3x) = 1
x^2 + 3x = 10
x^2 + 3x - 10 = 0
(x - 2) (x + 5) = 0
x = -5, won't work, so
x = 2
2007-04-23 02:39:14 · answer #4 · answered by ........ 5 · 0⤊ 0⤋
when you add logs you are multiplying
when you multiply logs you are raising to that power
2007-04-23 02:37:54 · answer #5 · answered by q6656303 6 · 0⤊ 0⤋