Find the solution of the exponential equation rounded to two

Find the solution of the exponential equation, rounded to two decimal places. (Enter your answers as comma separated lists.) 3^4x = 3^80 x = e^3x - 2 = e^x^2 x = 5^+1 = 8 x = 10^x +6 = 8^2x x =

Solution

a. 3^4x=3⁸⁰

    4x=80

     x=20

b. e^3x-2=e^{x^2}

   3x-2=x²

   x²-3x+2=0

   (x-2)(x-1)=0

    x=2,1

c. 5^x/14+1=8

   5^x/14=7

   taking log on both sides

   (x/14)log 5=log 7

    x/14= log7/log5

     x=14(log7/log5) =   16.93

d. 10^x+6=8^2x

     Taking log on both sides

    (x+6)log 10 = 2x log 8

    x+6= 2x log 8

         6= x(2log 8   -    1)

    x= 6/(2log 8    -1) = 7.44