2006-11-03 17:47:25 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
log(3x+8) - log(2x-5) = 2
First: since all expressions have to exist, it has to be that
3x+8 > 0 AND 2x-5 > 0. So x > 2.5
(3x+8) / (2x-5) = 100
3x + 8 = 200x - 500
508 = 197x
x = 2 + 114/197 = about 2.538.
This is the solution since 2.538 > 2.5
Number two is only an expression; no equation
log(x-5) + log(x+9) + log(x-6) + log(x-3)
Th
2006-11-03 18:01:04 · answer #1 · answered by Thermo 6 · 0⤊ 0⤋
A. Given: log(3x+8) - log(2x-5) = 2
We want to solve for x.
By applying some laws of logarithms to the expression on the left-hand side, we obtain
log[(3x + 8) / (2x - 5)] = 2.
This tells us that,
10^ { log[(3x + 8) / (2x - 5)] } = 10^2, that is
(3x + 8) / (2x - 5) = 100.
Equivalently,
3x + 8 = 100 (2x - 5).
= 200x - 500.
So,
3x - 200x = -500 - 8
-197x = -508
x = 508 / 197,
which is approximately 2.578.
Note that the value of x is a solution of the given equation if and only if:
log(3x + 8) is a real number whenever 3x + 8 > 0, i.e. x > -8/3 and
log(2x - 5) is a real number whenever 2x - 5 > 0, i.e. x > 5/2.
Since both inequalities must be satisfied, it implies that x > 5/2 = 2.5. Because our x in the above equation yields 508 / 197 > 2.5, it follows that x is a solution of the given equation.
B. Given: log(x-5) + log(x+9) + log(x-6) + log(x-3)
If we apply some laws on logarithms, we can only SIMPLIFY this into an expression with only one term, that is:
log [(x - 5)(x + 9)(x - 6)(x - 3)].
2006-11-04 02:26:34 · answer #2 · answered by rei24 2 · 0⤊ 0⤋
log(3x+8) - log(2x-5) = 2
log[(3x+8)/(2x-5)] = 2 (taking anti-logs).
(3x+8)/(2x-5) = 100
(3x+8) = 100(2x-5)
3x + 8 = 200x - 500
8 + 500 = 200x - 3x
508 = 197x
x = 508/197
x = 2â578 680 203
The second question is a statement, not an equation.
2006-11-04 03:03:31 · answer #3 · answered by Brenmore 5 · 0⤊ 0⤋
A1)log(3x+8) - log(2x-5)=2*1
we know that log(base a)a=1
therefore log(3x+8) - log(2x-5)=2log(base 10)10
=>log[(3x+8)/(2x-5)]=log[(10)^2]
removing log
(3x+8)/(2x-5)=100
=>3x+8=200x-500
=>197x=508
=>x=508/197
A2)log(x-5)+log(x+9)+log(x-6)+log(x-3)
reduces to log[(x-5)(x+9)(x-6)(x-3)]
2006-11-04 05:18:45 · answer #4 · answered by sushant 3 · 0⤊ 0⤋
In order from top to bottom:
(3x+8)-(2X5)=2
(3x+8)-10=2
but 3 should be 2. So...
(2x+8)-10=2
2X2+8-10=2
4+8-10=2
12-10=2
Then the next problem you didn't put what X equals.
2006-11-04 02:02:00 · answer #5 · answered by jglaroya 2 · 0⤊ 0⤋
log(3x+8) - log(2x-5) = 2
log(3x+8/2x-5)=2
100=3x+8/2x-5
i hope u can at least solve this.
2006-11-04 02:07:29 · answer #6 · answered by elvenprince 3 · 0⤊ 0⤋