Solve for x to two decimal places: 5000(1.09^12x) = 9500
2007-03-08 03:02:20 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1.09^12x=1.9
lg(1.09^12x)=lg1.9
12x=lg1.9/lg1.09
x=0.62
(lg=log to the base 10)
2007-03-08 03:08:31 · answer #1 · answered by Maths Rocks 4 · 0⤊ 0⤋
Divide both sides of the equation by 5000 first to simplify calculations. Then solve by using the properties of logarithms.
9500/5000 = 1.9
log (1.09^12x) = 12x [log (1.09)]
Now equate the right member of the last equation above with the log of 1.9, and then solve for x.
12x [log (1.09)] = log (1.9)
x = [log (1.9)] / 12 [log (1.09)]
2007-03-08 11:28:36 · answer #2 · answered by MathBioMajor 7 · 0⤊ 0⤋
5000*(1.09^(12*x)) = 9500
ln(5000) - 12*x*ln(1.09) = ln(9500)
x = (ln(5000) - ln(9500))/(12*ln(1.09))
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Doug
2007-03-08 11:08:52 · answer #3 · answered by doug_donaghue 7 · 0⤊ 0⤋