document.write( "Question 816636: Can you help me solve this problem \r
\n" ); document.write( "\n" ); document.write( "Solve. Log5 (3x+1)- Log5 4=2 \n" ); document.write( "

Algebra.Com's Answer #491661 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%285%2C+%283x%2B1%29%29-+log%285%2C%28+4%29%29=2\"$
\n" ); document.write( "First, use the $\"log%28a%2C%28p%29%29-log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29\"$ property to combine the logs:
\n" ); document.write( " $\"log%285%2C+%28%283x%2B1%29%2F4%29%29=2\"$
\n" ); document.write( "Then rewrite the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+n\"$ is equivalent to $\"p+=+a%5En\"$ . Using this pattern on our equation we get:
\n" ); document.write( " $\"%283x%2B1%29%2F4+=+5%5E2\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"%283x%2B1%29%2F4+=+25\"$
\n" ); document.write( "Now we solve this. Multiplying each side by 4 (to eliminate the fraction):
\n" ); document.write( "3x + 1 = 100
\n" ); document.write( "Subtracting 1:
\n" ); document.write( "3x = 99
\n" ); document.write( "Dividing by 3:
\n" ); document.write( "x = 33

\n" ); document.write( "Last, we check. This is not optional! A check must be made to ensure that the \"solution(s)\" make all bases and arguments of all logs valid. (Valid bases are any positive number except 1 and valid arguments are positive.) Any \"solution\" that makes any base or any argument invalid must be rejected.

\n" ); document.write( "Use the original equation to check:
\n" ); document.write( " $\"log%285%2C+%283x%2B1%29%29-+log%285%2C%28+4%29%29=2\"$
\n" ); document.write( "Checking x = 33:
\n" ); document.write( " $\"log%285%2C+%283%2833%29%2B1%29%29-+log%285%2C%28+4%29%29=2\"$
\n" ); document.write( "We can already see that the bases are 5's and the arguments are (or will end up) positive -- both valid. So this solution checks! \n" ); document.write( "

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