SOLUTION: solve each equation for x. a) 30= 80(1-e ^[-2x]) b) 5*2^x = 3^[x-1] c) log2(log3 x) = 5 d) e^[-1/2 log{x^(2)-1} = 1/square root3

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Question 1032379: solve each equation for x.
a) 30= 80(1-e ^[-2x])
b) 5*2^x = 3^[x-1]
c) log2(log3 x) = 5
d) e^[-1/2 log{x^(2)-1} = 1/square root3
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
solve each equation for x.
a) 30= 80(1-e ^[-2x])
I did this one yesterday.
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b) 5*2^x = 3^[x-1]
log(5) + x*log(2) = (x-1)*log(3) = x*log(3) - log(3)
log(5) + log(3) = x*log(3) - x*log(2)) = x*(log(3) - log(2)) = x*log(3/2)
x*log(1.5) = log(15)
x = log(15)/log(1.5)
x =~ 6.67887
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c) log2(log3 x) = 5
Not clear
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Assuming natural logs:
d) e^[-1/2 log{x^(2)-1} = 1/square root3
e^(-1/2) + e^ln(x^2-1) = 1/sqrt(3)
e^(-1/2) + x^2-1 = 1/sqrt(3)
x^2 = 1 - e^(-1/2) + 1/sqrt(3)
x^2 =~ 0.97081961
x =~ +0.9853
x =~ -0.9853