Solve each log equation.
(1) log_6 (36) = 5x + 3
(2) e^(-2x) = 1/3
2007-12-29 08:17:52 · 5 answers · asked by journey 1 in Science & Mathematics ➔ Mathematics
#1) use definition of log: 6^(5x+3) = 36
so, 5x+3 = 2
5x = -1
x= -1/5
#2) take the ln of both sides:
-2x ln e = ln 1/3
-2x = ln 1/3
x = (ln 1/3) /(-2) = ~0.5493
that's it! :)
2007-12-29 08:22:50 · answer #1 · answered by Marley K 7 · 0⤊ 0⤋
#1: log_6(36) = 2, so 2 = 5x + 3 or x = -1/5
#2: Take the natural log of both sides: -2x = ln(1/3) or x = -1/2 ln(1/3)
2007-12-29 16:22:59 · answer #2 · answered by Dynamic 4 · 0⤊ 0⤋
1. log base 6 of 36...
The rule to remember is, the logarithm is the power to which you raise the base to get the number. Memorize that and learn to apply it.
In this case, the log is the power to which you raise 6 to get 36. Of course that's 2. So...
2 = 5x + 3
That should be easy to solve from there.
2. take natural logs of both sides...
-2x = ln (1/3) = - ln 3
x = (ln 3) / 2
2007-12-29 16:26:43 · answer #3 · answered by Raichu 6 · 0⤊ 0⤋
(1) you can express it as 6^(5x+3) = 6^2
then 5x+3 = 2, and x = -1/5
(2) express it as ln 1/3 = -2x then use a calculator and you should get x = 0.549306....
2007-12-29 16:24:02 · answer #4 · answered by Anonymous · 0⤊ 0⤋
5x + 3 = 2
5x = -1
x = -1/5
-2x = ln 1/3, x = -0.55
2007-12-29 16:21:30 · answer #5 · answered by norman 7 · 0⤊ 0⤋