document.write( "Question 492964: Use natural logarithms to solve the equation 8*2^z=18*12^z for z (three decimal places). \n" ); document.write( "

Algebra.Com's Answer #335230 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
It can be simplified first
\n" ); document.write( " $\"+8%2A2%5Ez+=+18%2A12%5Ez+\"$
\n" ); document.write( "Divide both sides by $\"2\"$
\n" ); document.write( " $\"+4%2A2%5Ez+=+9%2A12%5Ez+\"$
\n" ); document.write( " $\"+%282%5Ez%29+%2F+%2812%5Ez%29+=+9%2F4+%7D%7D%0D%0A%7B%7B%7B+%282%2F12%29%5Ez+=+9%2F4+\"$
\n" ); document.write( " $\"+%281%2F6%29%5Ez+=+%283%2F2%29%5E2+\"$
\n" ); document.write( "Take the natural log of both sides
\n" ); document.write( " $\"+z%2Aln%281%2F6%29+=+2%2Aln%283%2F2%29+\"$
\n" ); document.write( " $\"+z+=+2%2A%28%28ln%283%2F2%29%29+%2F+ln%281%2F6%29%29+\"$
\n" ); document.write( " $\"+z+=+2%2A%28.405465+%2F+-1.79176%29+\"$
\n" ); document.write( " $\"+z+=+-.452589+\"$
\n" ); document.write( " $\"+z+=+-.453+\"$
\n" ); document.write( "check answer:
\n" ); document.write( " $\"+8%2A2%5E%28-.453%29+=+8%2A.7305+\"$
\n" ); document.write( " $\"+5.844+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+18%2A12%5E%28-.453%29+=+5.839+\"$
\n" ); document.write( "I think this is close enough\r
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