document.write( "Question 613652: Solve each equation. Show all your work. Round your answers to four decimal places.
\n" ); document.write( " a. 9^4x=81
\n" ); document.write( " b. log4(9x+5)-log4(2x+2)=1 \n" ); document.write( "

Algebra.Com's Answer #386122 by radh(108) $\"\"$ $\"About$

You can put this solution on YOUR website!
a. Create equivalent expressions so that they all have equal bases.
\n" ); document.write( " $\"3%5E%282%284x%29%29=3%5E%284%29\"$
\n" ); document.write( "Since the bases are the same, we can cancel them out.
\n" ); document.write( " $\"2%284x%29=4\"$
\n" ); document.write( "Divide.
\n" ); document.write( " $\"%282%284x%29%29%2F%282%29=%284%29%2F%282%29\"$
\n" ); document.write( "Multiply.
\n" ); document.write( " $\"%288x%29%2F%282%29=%284%29%2F%282%29\"$
\n" ); document.write( "Divide and simplify.
\n" ); document.write( " $\"4x=2\"$
\n" ); document.write( "Divide and simplify again.
\n" ); document.write( " $\"x=%282%29%2F%284%29\"$
\n" ); document.write( "Reduce the fraction.
\n" ); document.write( " $\"x=%281%29%2F%282%29\"$ \r
\n" ); document.write( "\n" ); document.write( "

b.
\n" ); document.write( "Multiply continuously.
\n" ); document.write( " $\"%28log4%289x%29%2Blog4%285%29%29-log4%282x%2B2%29=1\"$
\n" ); document.write( " $\"%28log4%2A9x%2Blog4%285%29%29-log4%282x%2B2%29=1\"$
\n" ); document.write( " $\"%289xlog4%2Blog4%285%29%29-log4%282x%2B2%29=1\"$
\n" ); document.write( " $\"%289xlog4%2Blog4%2A5%29-log4%282x%2B2%29=1\"$
\n" ); document.write( " $\"%289xlog4%2B5log4%29-log4%282x%2B2%29=1\"$
\n" ); document.write( " $\"%289xlog4%2B5log4%29%2B%28-log4%282x%29-log4%282%29%29=1\"$
\n" ); document.write( " $\"%289xlog4%2B5log4%29%2B%28-log4%2A2x-log4%282%29%29=1\"$
\n" ); document.write( " $\"%289xlog4%2B5log4%29%2B%28-2xlog4-log4%282%29%29=1\"$
\n" ); document.write( " $\"%289xlog4%2B5log4%29%2B%28-2xlog4-log4%2A2%29=1\"$
\n" ); document.write( " $\"%289xlog4%2B5log4%29%2B%28-2xlog4-2log4%29=1\"$
\n" ); document.write( "Use the distributive property.
\n" ); document.write( " $\"7xlog4%2B%285-2%29log4=1\"$
\n" ); document.write( "Simplify.
\n" ); document.write( " $\"7xlog4%2B3log4=1\"$
\n" ); document.write( "Subtract to the other side.
\n" ); document.write( " $\"7xlog4=-3log4%2B1\"$
\n" ); document.write( "Use the third law of logarithms.
\n" ); document.write( " $\"7xlog4=log%284%5E%28-3%29%29%2B1\"$
\n" ); document.write( "Remove the negative exponent.
\n" ); document.write( " $\"7xlog4=log%28%281%29%2F%284%5E%283%29%29%29%2B1\"$
\n" ); document.write( "Cube 4 (Simplify)
\n" ); document.write( " $\"7xlog4=log%28%281%29%2F%2864%29%29%2B1\"$
\n" ); document.write( "Move all the terms (containing a log) to the left-hand side of the equation.
\n" ); document.write( " $\"7xlog4-log%28%281%29%2F%2864%29%29=1\"$ \r
\n" ); document.write( "\n" ); document.write( "

:) \n" ); document.write( "

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