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

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.
---------------
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
==============
c) log2(log3 x) = 5
Not clear
=================
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

RELATED QUESTIONS
Solve each equation for x. (a) 30 = 80(1 − e^−2x) (b) 5 � 2^x = 3^... (answered by Alan3354)

Solve each equation for x. (a) 30 = 80(1 − e^−2x) (b) 5 X 2^x = 3^... (answered by stanbon)

Solve for x in each: A) 9^(2x+3) =81^(2x-1) B)2log2x=log(7x-3) C)7*3^(x+2)=5x... (answered by Edwin McCravy)

Solve. 5(x-2)^2=3 a. 1/5 19/5 b. 10+-square root15over 5 c. 10+-square root3... (answered by jim_thompson5910,edjones)

Solve each equation for x A. 27^X=3^X+1 B. e^3x-1=12 C.log(x+3)-log x=log 2 D.log5 X+ (answered by jim_thompson5910)

log8(3x-2)=2 log2(4x)-log2(3=6) 4e^2x+1=12 log6(x+6)+log6(2=2) log3[log2(x+5)]=1... (answered by stanbon)

4/2x+1 - 2/x-2 = 1/2x+1 Solve rational equation a.-10 b.-17 c.-5 d.-8... (answered by sofiyac)

4/(2x+1) - 2/(x-2) = 1/(2x+1) Solve rational equation a.-10 b.-17 c.-5 d.-8... (answered by ewatrrr)

(a) (4x+2)(2x) = 32 (b) (3x+2)(9x+3) = 81 (c) log (x-3) + log (x) = 1 (d) log2 (answered by jim_thompson5910)