Question 613652
a. Create equivalent expressions so that they all have equal bases.
{{{3^(2(4x))=3^(4)}}}
Since the bases are the same, we can cancel them out.
{{{2(4x)=4}}}
Divide.
{{{(2(4x))/(2)=(4)/(2)}}}
Multiply.
{{{(8x)/(2)=(4)/(2)}}}
Divide and simplify.
{{{4x=2}}}
Divide and simplify again.
{{{x=(2)/(4)}}}
Reduce the fraction.
{{{x=(1)/(2)}}}

<p>b. 
Multiply continuously.
{{{(log4(9x)+log4(5))-log4(2x+2)=1}}}
{{{(log4*9x+log4(5))-log4(2x+2)=1}}}
{{{(9xlog4+log4(5))-log4(2x+2)=1}}}
{{{(9xlog4+log4*5)-log4(2x+2)=1}}}
{{{(9xlog4+5log4)-log4(2x+2)=1}}}
{{{(9xlog4+5log4)+(-log4(2x)-log4(2))=1}}}
{{{(9xlog4+5log4)+(-log4*2x-log4(2))=1}}}
{{{(9xlog4+5log4)+(-2xlog4-log4(2))=1}}}
{{{(9xlog4+5log4)+(-2xlog4-log4*2)=1}}}
{{{(9xlog4+5log4)+(-2xlog4-2log4)=1}}}
Use the distributive property.
{{{7xlog4+(5-2)log4=1}}}
Simplify.
{{{7xlog4+3log4=1}}}
Subtract to the other side.
{{{7xlog4=-3log4+1}}}
Use the third law of logarithms. 
{{{7xlog4=log(4^(-3))+1}}}
Remove the negative exponent.
{{{7xlog4=log((1)/(4^(3)))+1}}}
Cube 4 (Simplify)
{{{7xlog4=log((1)/(64))+1}}}
Move all the terms (containing a log) to the left-hand side of the equation.
{{{7xlog4-log((1)/(64))=1}}}

<p>:)