How do you slove this???
lg(2x)-3lg2=(1/2)lg(x-3)
lg means log with base 10
2007-11-03 17:52:59 · 3 answers · asked by A A 1 in Science & Mathematics ➔ Mathematics
log(2x) - 3log(2) = (1/2)log(x-3)
log(2x) - log(2^3) = log((x-3)^(1/2))
log(2x/8) = log(sqrt(x-3))
log(x/4) = log(sqrt(x-3))
x/4 = sqrt(x-3)
x = 4sqrt(x-3)
x^2 = 16(x-3)
x^2 - 16x + 48 = 0
(x-12)(x-4) = 0
possible x values are 12 and 4
if you check them both, 12 works, but 4 doesnt.
So the answer is x = 12.
2007-11-03 18:02:31 · answer #1 · answered by Anonymous · 0⤊ 0⤋
regmcube is correct, except that 4 works as well as 12:
log(8) - log(8) = (1/2)log(1)
2007-11-03 18:24:51 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋
make the left hand side one logarithm, then exponentiate both sides.
2007-11-03 18:01:52 · answer #3 · answered by bassbrobrad 1 · 0⤊ 0⤋