Question 1205634
.
log base 4 of y + log base2 of y =12
solve for y
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<pre>
Your starting equation is

    {{{log(4,(y))}}} + {{{log(2,(y))}}} = 12.    (1)


Use the base change formula

    {{{log(2,(y))}}} = {{{log(4,(y))/log(4,(2))}}} = {{{log(4,(y))/((1/2))}}} = {{{2*log(4,(y))}}}.


Therefore, equation (1) takes the form

    {{{log(4,(y))}}} + {{{2*log(4,(y))}}} = 12

    {{{3*log(4,(y))}}} = 12

    {{{log(4,(y))}}} = 12/3 = 4

    y = {{{4^4}}} = 256.


<U>ANSWER</U>.  y = 256.
</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.