document.write( "Question 749560: I can not seem to figure this question out...\r
\n" ); document.write( "\n" ); document.write( "log[4](x+3)-log[4](x+2) >= 3/2 \n" ); document.write( "

Algebra.Com's Answer #456122 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
For $\"log%284%2C%28x%2B3%29%29\"$ and $\"log%284%2C%28x%2B2%29%29\"$ to exist, it must be that $\"x%2B3%3Ex%2B2%3E0\"$ <--> $\"x%3E-2\"$
\n" ); document.write( "(because logarithm exist only for positive numbers).
\n" ); document.write( " $\"log%284%2C%28x%2B3%29%29-log%284%2C%28x%2B2%29%29%3E=3%2F2\"$ --> $\"log%284%2C%28%28x%2B3%29%2F%28x%2B2%29%29%29%3E=3%2F2\"$ --> $\"%28x%2B3%29%2F%28x%2B2%29%3E=4%5E%283%2F2%29\"$ --> $\"%28x%2B3%29%2F%28x%2B2%29%3E=%282%5E2%29%5E%283%2F2%29\"$ --> $\"%28x%2B3%29%2F%28x%2B2%29%3E=2%5E%28%282%2A3%2F2%29%29\"$ --> $\"%28x%2B3%29%2F%28x%2B2%29%3E=2%5E3\"$ --> $\"%28x%2B3%29%2F%28x%2B2%29%3E=8\"$
\n" ); document.write( "Since $\"x%2B2%3E0\"$ , multiplying both sides times $\"%28x%2B2%29\"$ does not require flipping the inequality sign, so
\n" ); document.write( " $\"%28x%2B3%29%2F%28x%2B2%29%3E=8\"$ --> $\"x%2B3%3E=8%2A%28x%2B2%29\"$ --> $\"x%2B3%3E=8x%2B16\"$ --> $\"3-16%3E=8x-x\"$ --> $\"-13%3E=7x\"$ --> $\"-13%2F7%3E=x\"$
\n" ); document.write( "The solution is $\"highlight%28-2%3Cx%3C=-13%2F7%29\"$ \n" ); document.write( "

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