Question 1200017
.
Solve the following exponential equations
a) 3^x=5(2^x)
b) 9^(x-1)*3^x=27
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<pre>
(a)  {{{3^x}}} = {{{5*2^x}}}.

     Take logarithm base 10 of both sides. Use properties of logarithms.  You will get

     x*log(3) = log(5) + x*log(2)

     x*log(3) - x*log(2) = log(5)

     x*(log(3) - log(2)) = log(5)

     x = {{{log((5))/(log((3))-log((2)))}}} = 3.969  (rounded).    <U>ANSWER</U>



(b)  {{{9^(x-1)*3^x}}} = {{{27}}}


     It is the same as

     {{{(3^2)^(x-1)*3^x}}} = {{{27}}}

     {{{3^(2(x-1))*3^x}}} = {{{3^3}}}

     {{{3^(2x-2+x)}}} = {{{3^3}}}

     {{{3^(3x-2)}}} = {{{3^3}}}


     The base is 3 in both sides of the equation - hence, the degrees are identical

     3x-2 = 3

     3x = 3+2 = 5

      x       = {{{5/3}}}.    <U>ANSWER</U>
</pre>

Solved.


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On logarithms and their properties, &nbsp;see these introductory lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/what-is-the-logarithm.lesson>WHAT IS the logarithm</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/Properties-of-the-logarithm.lesson>Properties of the logarithm</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/change-of-base-formula-for-logarithms.lesson>Change of Base Formula for logarithms</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Evaluate-logarithms-without-using-a-calculator.lesson>Evaluate logarithms without using a calculator</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Simplifying-expressions-with-logarithms.lesson>Simplifying expressions with logarithms</A> 

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

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Logarithms</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.