Lesson OVERVIEW of lessons on solving exponential equations

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> Lesson OVERVIEW of lessons on solving exponential equations      Log On


   

This Lesson (OVERVIEW of lessons on solving exponential equations) was created by by ikleyn(52778) About Me : View Source, Show
About ikleyn:

OVERVIEW of lessons on solving exponential equations


In this site,  there are lessons on solving exponential equations and related problems

    - Solving exponential equations
    - Solving advanced exponential equations
    - Solving exponential inequalities
    - Solving upper level exponential equations
    - Joke problem on solving exponential equation
    - Solving problems on population growth using logistic functions

List of lessons with short annotations


Solving exponential equations

        Problem 1.  Solve an equation   9%5E%28x%2B1%29 = 81%5E%282x%2B1%29.

        Problem 2.  Solve an equation   2%5E%282x%5E2%2B2%29+=+2%5E%285x%29.

        Problem 3.  Solve an equation  %280.5%5E%28x-0.5%29%29%2Fsqrt%282%29 = 2%2A0.25%5E%28x-1%29.

        Problem 4.  Solve an equation  9%5Ex%2B3%5E%28x%2B1%29+-+108 = 0.

        Problem 5.  Solve an equation for x:  3%5E%28x%2B1%29+-+4 + 1%2F3%5Ex = 0.

        Problem 6.  Solve an equation  3%5E%282y%2B1%29 - 13%283%5Ey%29 + 4 = 0.

        Problem 7.  Solve an equation   5%5E%282x%2B1%29+%2B+25 = 5%5E%28x%2B3%29+%2B+5%5Ex

        Problem 8.  Solve an equation   2%2A2%5E%282x%29 - 5%2A2%5Ex%29 + 2 = 0.

        Problem 9.  Solve an equation   3e%5Ex = 5 + 8e%5E%28-x%29.


Solving advanced exponential equations

        Problem 1.  Solve an equation   3%5Ex + 3%5E%28x%2B1%29 = 11%5Ex + 11%5E%28x%2B1%29.

        Problem 2.  Solve an equation   4%5E%28x%2B1.5%29 + 9%5E%28x%2B0.5%29 = 10%2A6%5Ex.

        Problem 3.  Solve an equation   4%5Ex + 6%5Ex = 9%5Ex.

        Problem 4.  Solve an equation   16%5Esin%5E2%28x%29 + 16%5Ecos%5E2%28x%29 = 10.

        Problem 5.  Solve an equation   sqrt%28x%29%5Ex = x%5Esqrt%28x%29.

        Problem 6.  If   %28x%2Asqrt%28x%29%29%5E%281%2Fx%29+=+2,   find x.


Solving exponential inequalities

        Problem 1.  Solve the following exponential inequality   %28root%283%2C10%29%29%5E%281-2x%29 > 0.1%5E%282x%2B1%29.

        Problem 2.  Find the smallest positive integer  n  such that the base ten representation of  2  at the power of  n  has exactly  500  digits.


Solving upper level exponential equations

        Problem 1.  Solve an equation   log%289%2C%284%5Ex-2%2A18%5Ex%29%29 = 2x.

        Problem 2.  Solve for  x,   9%5Ex = x%5E6,   x > 0.

        Problem 3.  Solve for  x,   81%5Ex = x%5E18,   x > 0.

        Problem 4.  Find x,   3%5Ex = x%5E9,   x > 0.

        Problem 5.  Find x,   9%5Ex = x%5E5,   x > 0.

        Problem 6.  Find the solutions to this equation   4%5Esin%5E2%28x%29 + 4%5Ecos%5E2%28x%29 = 3%2Asqrt%282%29.

        Problem 7.  Solve this system of equations
                               2%5Ex + 2%5Ey = 40,
                               x   +   y   =   8.
                           Find  x  and  y.


Joke problem on solving exponential equation

        Problem 1.  Solve this exponential equation and find  x:   3^[(x+1)/(x-5)] + 3^[(3x-9)/(x-5)] = 10/3.

        Problem 2.  If   x^(x¹⁶) = 16,  find   x²⁰.

        Problem 3.  If   2^a = 3,  3^b = 2,   find   1/(a+1) + 1/(b+1).


Solving problems on population growth using logistic functions

        Problem 1.  Assume there is a certain population of fish in a pond whose growth is described by the logistic equation.
                           It is estimated that the carrying capacity for the pond is  1600  fish.  Absent constraints,
                           the population would grow by  120%  per year.
                           If the starting population is given by  P0 = 200,  then estimate fish population after one and two years.


Use this file/link  ALGEBRA-I - YOUR ONLINE TEXTBOOK  to navigate over all topics and lessons of the online textbook  ALGEBRA-I.

This lesson has been accessed 1870 times.