document.write( "Question 563657: use natural logarithms to solve the equation 7 (3^z) = 19 (15^z) for z (three decimal places) \n" ); document.write( "

Algebra.Com's Answer #365139 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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use natural logarithms to solve the equation 7 (3^z) = 19 (15^z) for z (three decimal places)
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\n" ); document.write( " $\"7+%283%5Ez%29+=+19+%2815%5Ez%29\"$
\n" ); document.write( "divide both sides by 7
\n" ); document.write( " $\"3%5Ez+=+%2819%2F7%29+15%5Ez\"$
\n" ); document.write( "Divide both sides by 15^z
\n" ); document.write( " $\"3%5Ez%2F15%5Ez+=+19%2F7\"$
\n" ); document.write( "Which is
\n" ); document.write( " $\"%283%2F15%29%5Ez+=+19%2F7\"$
\n" ); document.write( "Reduce the fraction
\n" ); document.write( " $\"%281%2F5%29%5Ez+=+19%2F7\"$
\n" ); document.write( "using nat logs
\n" ); document.write( " $\"ln%28%281%2F5%29%5Ez%29+=+ln%2819%2F7%29\"$
\n" ); document.write( "log equiv of exponents
\n" ); document.write( " $\"z%2Aln%281%2F5%29+=+ln%2819%2F7%29\"$
\n" ); document.write( "find the ln
\n" ); document.write( "-1.6094z = .9985
\n" ); document.write( "z = $\".9985%2F%28-1.6094%29\"$
\n" ); document.write( "z = -.6206
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\n" ); document.write( "Check solution on a calc:
\n" ); document.write( "enter 7*3^-.62) = 3.54
\n" ); document.write( "enter 19*15^-.62 = 3.54; confirms our solution of z = -.6206\r
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