SOLUTION: Solve each equation for x.
(a) 30 = 80(1 − e^−2x)
(b) 5 X 2^x = 3^ (x−1) ; ( here capital X is for multiply )
(c) log2(log3 x) = 5 ; ( here 2 and 3 are bases
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-> SOLUTION: Solve each equation for x.
(a) 30 = 80(1 − e^−2x)
(b) 5 X 2^x = 3^ (x−1) ; ( here capital X is for multiply )
(c) log2(log3 x) = 5 ; ( here 2 and 3 are bases
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Question 1032611: Solve each equation for x.
(a) 30 = 80(1 − e^−2x)
(b) 5 X 2^x = 3^ (x−1) ; ( here capital X is for multiply )
(c) log2(log3 x) = 5 ; ( here 2 and 3 are bases of the logs )
(d) e^− 1/2log(x^2 − 1) =1/ sqrt 3 Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Solve each equation for x.
(a) 30 = 80(1 − e^−2x)
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1-e^(-2x) = 3/8
e^(-2x) = 5/8
-2x = ln(5/8)
-2x = -0.47
x = 0.235
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(b) 5 X 2^x = 3^ (x−1) ; ( here capital X is for multiply )
log(5) + x*log(2) = (x-1)log(3)
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log(5) + x*log(2) = x*log(3) - log(3)
x(log(2)-log(3)) = -[log(3)+log(5)]
x = -[log(3)+log(5)]/[log(2)-log(3)]I'll leave the arithmetic to you.
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(c) log2(lo3 x) = 5 ; ( here 2 and 3 are bases of the logs )
log2[log(x)/log(3)] = 5
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log2[log(x)] - log2[log(3)] = 5
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log2[log(x)] - log2[0.4771] = 5
log2[log(x)] - log(0.4771)/log(2) = 5
log2[log(x)] + 1.0676 = 5
log2[log(x)] = 3.9324
log(x) = 2^3.9324 = 15.2672
x = 10^15.2672 = 1.85..x10^15
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(d) e^− 1/2*log(x^2 − 1) =1/ sqrt 3
0.6065*log(x^2-1) = 0.5774
log(x^2-1) = 0.9519
x^2-1 = 10^0.9519 = 8.9523
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x^2 = 9.9523
x = 3.1547
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