Lesson OVERVIEW of lessons on solving exponential equations

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<H2>OVERVIEW of lessons on solving exponential equations</H2>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/How-to-solve-exponential-equations.lesson>Solving exponential equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Solving-advanced-exponential-equations.lesson>Solving advanced exponential equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Solving-exponential-inequalities.lesson>Solving exponential inequalities</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Solving-upper-level-exponential-equations.lesson>Solving upper level exponential equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Joke-problem-on-solving-exponential-equatioin.lesson>Joke problem on solving exponential equation</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Solving-problems-on-population-growth-using-logistic-function.lesson>Solving problems on population growth using logistic functions</A>

<H3>List of lessons with short annotations</H3>
<A HREF=https://www.algebra.com/algebra/homework/logarithm/How-to-solve-exponential-equations.lesson>Solving exponential equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Solve an equation &nbsp;&nbsp;{{{9^(x+1)}}} = {{{81^(2x+1)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;Solve an equation &nbsp;&nbsp;{{{2^(2x^2+2) = 2^(5x)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;Solve an equation &nbsp;{{{(0.5^(x-0.5))/sqrt(2)}}} = {{{2*0.25^(x-1)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;Solve an equation &nbsp;{{{9^x+3^(x+1) - 108}}} = {{{0}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;Solve an equation for x: &nbsp;{{{3^(x+1) - 4}}} + {{{1/3^x}}} = {{{0}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;Solve an equation &nbsp;{{{3^(2y+1)}}} - {{{13(3^y)}}} + {{{4}}} = {{{0}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 7. &nbsp;Solve an equation &nbsp;&nbsp;{{{5^(2x+1) + 25}}} = {{{5^(x+3) + 5^x}}}

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 8. &nbsp;Solve an equation &nbsp;&nbsp;{{{2*2^(2x)}}} - {{{5*2^x)}}} + {{{2}}} = {{{0}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 9. &nbsp;Solve an equation &nbsp;&nbsp;{{{3e^x}}} = {{{5}}} + {{{8e^(-x)}}}.

<A HREF=https://www.algebra.com/algebra/homework/logarithm/Solving-advanced-exponential-equations.lesson>Solving advanced exponential equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Solve an equation &nbsp;&nbsp;{{{3^x}}} + {{{3^(x+1)}}} = {{{11^x}}} + {{{11^(x+1)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;Solve an equation &nbsp;&nbsp;{{{4^(x+1.5)}}} + {{{9^(x+0.5)}}} = {{{10*6^x}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;Solve an equation &nbsp;&nbsp;{{{4^x}}} + {{{6^x}}} = {{{9^x}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;Solve an equation &nbsp;&nbsp;{{{16^sin^2(x)}}} + {{{16^cos^2(x)}}} = {{{10}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;Solve an equation &nbsp;&nbsp;{{{sqrt(x)^x}}} = {{{x^sqrt(x)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;If &nbsp;&nbsp;{{{(x*sqrt(x))^(1/x) = 2}}}, &nbsp;&nbsp;find x.

<A HREF=https://www.algebra.com/algebra/homework/logarithm/Solving-exponential-inequalities.lesson>Solving exponential inequalities</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Solve the following exponential inequality &nbsp;&nbsp;{{{(root(3,10))^(1-2x)}}} > {{{0.1^(2x+1)}}}.

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

<A HREF=https://www.algebra.com/algebra/homework/logarithm/Solving-upper-level-exponential-equations.lesson>Solving upper level exponential equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Solve an equation &nbsp;&nbsp;{{{log(9,(4^x-2*18^x))}}} = 2x.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;Solve for &nbsp;x, &nbsp;&nbsp;{{{9^x}}} = {{{x^6}}}, &nbsp;&nbsp;x > 0.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;Solve for &nbsp;x, &nbsp;&nbsp;{{{81^x}}} = {{{x^18}}}, &nbsp;&nbsp;x > 0.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;Find x, &nbsp;&nbsp;{{{3^x}}} = {{{x^9}}}, &nbsp;&nbsp;x > 0.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;Find x, &nbsp;&nbsp;{{{9^x}}} = {{{x^5}}}, &nbsp;&nbsp;x > 0.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;Find the solutions to this equation &nbsp;&nbsp;{{{4^sin^2(x)}}} + {{{4^cos^2(x)}}} = {{{3*sqrt(2)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 7. &nbsp;Solve this system of equations

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{2^x}}} + {{{2^y}}} = 40,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find &nbsp;x &nbsp;and &nbsp;y.

<A HREF=https://www.algebra.com/algebra/homework/logarithm/Joke-problem-on-solving-exponential-equatioin.lesson>Joke problem on solving exponential equation</A>

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

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

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

<A HREF=https://www.algebra.com/algebra/homework/logarithm/Solving-problems-on-population-growth-using-logistic-function.lesson>Solving problems on population growth using logistic functions</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Assume there is a certain population of fish in a pond whose growth is described by the logistic equation.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is estimated that the carrying capacity for the pond is &nbsp;1600 &nbsp;fish. &nbsp;Absent constraints,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the population would grow by &nbsp;120% &nbsp;per year.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If the starting population is given by &nbsp;P0 = 200, &nbsp;then estimate fish population after one and two years.

Use this file/link &nbsp;<A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>&nbsp; to navigate over all topics and lessons of the online textbook &nbsp;ALGEBRA-I.