Solve each log equation.
(1) Ine^(-2x) = 8
(2) log_5 (626) = x
2007-12-29 08:13:50 · 4 answers · asked by journey 1 in Science & Mathematics ➔ Mathematics
NOTE: Question 2 is (625) NOT (626) in parentheses. See it?
2007-12-29 08:15:11 · update #1
(1) Ine^(-2x) = 8
Note that lne^x =x, so we get
Ine^(-2x) = 8
-2x=8 --> x= -4
(2) log_5 (626) = x is the same as 5^x = 626, so
5^x = 626
Logging both sides, we get
5^x=626
xlog5=log626
x=log626/log5 ~4.000993341
2007-12-29 08:17:13 · answer #1 · answered by ¿ /\/ 馬 ? 7 · 0⤊ 0⤋
1)lne^(-2x) simplfies to -2x because you move the exponent to the front of the equation. Then lne simplfies to one because its like saying "what power must you take e to get e?" which is one.
So..
lne^(-2x)=8
-2x=8
x=-4
2) if you can use a calculator then its 4. If not, then the variable x is what power you need to take the base, in this case 5, to get the number in the parenthases, 625. You have to multiply 5 by itself 4 times to get 625.
2007-12-29 16:21:57 · answer #2 · answered by E D 2 · 0⤊ 0⤋
-2x = 8, x = -4
625 = 5^4, x = 4
2007-12-29 16:19:18 · answer #3 · answered by norman 7 · 0⤊ 0⤋
1) lne^(-2x)=8
e^8=e^(-2x)
-2x=8
x= -4 - result
2007-12-29 16:30:52 · answer #4 · answered by sweetreddevil 1 · 0⤊ 0⤋