Asked by Ubon
Solve each exponential equation. Give answers as decimals accurate to the thousands place.
1) log(base5)14=2x-9
2) log(base7)5=7-6x
3) (1/3)^(3x+5)=(9)^(8-x)
4) 4^(x-5)=8^(x+2)
1) log(base5)14=2x-9
2) log(base7)5=7-6x
3) (1/3)^(3x+5)=(9)^(8-x)
4) 4^(x-5)=8^(x+2)
Answers
Answered by
Damon
so did you try?
Answered by
Ubon
i tried 3 and 4 but im not sure if its correct
3) -21
4) -16
and im not sure how to do 1 and 2
3) -21
4) -16
and im not sure how to do 1 and 2
Answered by
Damon
1) for example:
log5 (14) = 2x-9
5^[log5 (14)] = 14 = 5^(2x-9)
so the question is
5 to the what = 14 ?
say 5^z = 14 (we know that z is (2x-9))
z log 5 = log 14 using base 10 logs (or e or whatever, I use base 10)
z = log14/log5 = 1.146 / .699 = 1.64
so
2x-9 = 1.64
2x = 10.64
x = 5.32
log5 (14) = 2x-9
5^[log5 (14)] = 14 = 5^(2x-9)
so the question is
5 to the what = 14 ?
say 5^z = 14 (we know that z is (2x-9))
z log 5 = log 14 using base 10 logs (or e or whatever, I use base 10)
z = log14/log5 = 1.146 / .699 = 1.64
so
2x-9 = 1.64
2x = 10.64
x = 5.32
Answered by
Damon
try 3)
(1/3)^(3x+5)=(9)^(8-x)
(3x+5) log .333333333 = (8-x) log 9
(3x+5)(-.4771) = (8-x) (.9542)
(3x+5) = (x-8) 2 that was lucky :)
3 x + 5 = 2x-16
x = -21 agree
=====================
or this way
(1/3)^(3x+5)=(9)^(8-x)
1^(3x+5)/3^(3x+5) = 3^(16-2x)
1 = 3^(x+21)
x+21 = 0
x = -21
(1/3)^(3x+5)=(9)^(8-x)
(3x+5) log .333333333 = (8-x) log 9
(3x+5)(-.4771) = (8-x) (.9542)
(3x+5) = (x-8) 2 that was lucky :)
3 x + 5 = 2x-16
x = -21 agree
=====================
or this way
(1/3)^(3x+5)=(9)^(8-x)
1^(3x+5)/3^(3x+5) = 3^(16-2x)
1 = 3^(x+21)
x+21 = 0
x = -21
Answered by
Damon
4) 4^(x-5)=8^(x+2)
(2^2)^(x-5) = (2^3)^(x+2)
2^(2x-10) = 2^(3x+6)
2x-10 = 3x+6
x = -16 agree
(2^2)^(x-5) = (2^3)^(x+2)
2^(2x-10) = 2^(3x+6)
2x-10 = 3x+6
x = -16 agree
Answered by
Damon
2) log(base7)5=7-6x
5 = 7^(7-6x) = 7^z
log 5 = z log 7
z = .827
7 - 6 x = .827
6 x = 6.1729
x = 1.0288
5 = 7^(7-6x) = 7^z
log 5 = z log 7
z = .827
7 - 6 x = .827
6 x = 6.1729
x = 1.0288
Answered by
Steve
or, for #1, just change the base to one you know
log_5(14) = log14/log5 = 1.64
now you are already at
2x-9 = 1.64
log_5(14) = log14/log5 = 1.64
now you are already at
2x-9 = 1.64
Answered by
Felipe
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