Solve the equation algebraically. Support your answer numerically.
2007-04-04 03:34:32 · 4 answers · asked by Ducky 1 in Science & Mathematics ➔ Mathematics
40 [(1/2)^ (x/13)] = 10.
40[(1/2)^(x/13)]/40 = 10/40.
(1/2)^(x/13) = 1/4.
x/13 = 2.
(13)(x/13) = (13)(2).
x = (13)(2).
x = 26.
40[(1/2)^(26/13)] = 10.
40[(1/2)^(2)] = 10.
40[(1/2)(1/2)] =10.
40 (1/4) = 10.
40/4 = 10.
10 = 10
2007-04-04 03:58:36 · answer #1 · answered by Mark 6 · 0⤊ 0⤋
Is the equation meant to be 40*(1/2)^(x/13) = 10, with (x/13) as the exponent? It's important to show it that way, if it is. Start by dividing both sides by 40. Then take the log base (1/2) of both sides. Or, if you prefer, write the right hand side as (1/2) raised to an exponent, and then set the exponents of (1/2) on both sides as equal. Then solve using simple algebra.
40*(1/2)^(x/13) = 10
(1/2)^(x/13) = 1/4
x/13 = 2
x = 26
Numerical support: 40*(1/2)^(26/13) = 40*(1/2)^2 = 40*(1/4) = 10, QED.
2007-04-04 03:40:33 · answer #2 · answered by DavidK93 7 · 0⤊ 0⤋
Divide by 40.
(1/2)^(x/13) = .25
Ln both sides
ln(.5)^(x/13) = ln(.25)
move exponent to the front.
(x/13)*Ln(.5) = ln(.25)
simplify
x = 13 * ln(.5) / ln(.25)
2007-04-04 03:40:28 · answer #3 · answered by Big D's Tuna 2 · 0⤊ 1⤋
-1.700439718
Please give me best answer thanks!
2007-04-04 04:13:10 · answer #4 · answered by Anonymous · 0⤊ 0⤋