How to solve for t? #3e^t=5+8e^(-t)#

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Answer 1 · 2018-04-25T12:27:37

Solution: # t ~~ 0.98#

# 3 e^t=5+8 e^(-t)# Multiplying by #e^t# on both sides we get,

# 3 e^(2 t)=5 e^t+8 # or

# 3 e^(2 t) - 5 e^t- 8 = 0# or

# 3 e^(2 t) + 3 e^t -8 e^t - 8 = 0# or

# 3 e^ t( e^t +1) - 8( e^t + 1) = 0# or

#( e^t +1)(3 e^t - 8) = 0#

#:. e^t = -1 or 3 e^t =8 ; e^t# cannot be negative number

#:. e^t =8/3 #, taking natural log on both sides we get,

#t ln e = ln 8 - ln 3 :. t = ln 8 - ln 3 ~~ 0.98 (2 dp)[ ln e=1]#

Solution: # t ~~ 0.98# [Ans]

Answer 2 · 2018-04-25T12:33:11

#t=ln(8/3)~~0.9808#

Here,

#3e^t=5+8e^-t#

#=>3e^t=5+8/(e^t)#

#=>3(e^t)^2=5e^t+8#

#=>3(e^t)^2-5e^t-8=0#

#=>3(e^t)^2+3e^t-8e^t-8=0#

#=>3e^t(e^t+1)-8(e^t+1)=0#

#=>(e^t+1)(3e^t-8)=0#

#=>e^t+1=0 or 3e^t-8=0#

#=>e^t=-1 or e^t=8/3#

#(i)e^t=-1 <0=>e^t !inR^+#

#(ii)e^t=8/3=>t=ln(8/3)~~0.9808#