document.write( "Question 718243: What is the approximate solution to 5^6x+3=37? This means 5 with the exponents of 5 being 6x+3 and the answer equaling 37.
\n" ); document.write( "Any help is appreciated.\r
\n" ); document.write( "\n" ); document.write( "Thanks,\r
\n" ); document.write( "\n" ); document.write( "Sherry \n" ); document.write( "

Algebra.Com's Answer #440847 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
First of all, if you put multiple-term exponents in parentheses:
\n" ); document.write( "5^(6x+3)=37
\n" ); document.write( "you don't have to explain what the exponent is.

\n" ); document.write( " $\"5%5E%286x%2B3%29=37\"$
\n" ); document.write( "To find a decimal approximation for the solution we will be using logarithms, specifically logs your calculator \"knows\" (base e, \"ln\", or base 10, \"log):
\n" ); document.write( " $\"ln%285%5E%286x%2B3%29%29=ln%2837%29\"$
\n" ); document.write( "Next we use a property of logarithms, $\"log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29\"$ , which allows us to move the exponent of the argument out in front (where can then \"get at\" the variable):
\n" ); document.write( " $\"%286x%2B3%29%2Aln%285%29=ln%2837%29\"$
\n" ); document.write( "Dividing by ln(5):
\n" ); document.write( " $\"6x%2B3=ln%2837%29%2Fln%285%29\"$
\n" ); document.write( "Subtract 3:
\n" ); document.write( " $\"6x=ln%2837%29%2Fln%285%29-3\"$
\n" ); document.write( "Divide by 6:
\n" ); document.write( " $\"x=%28ln%2837%29%2Fln%285%29-3%29%2F6\"$
\n" ); document.write( "This is an exact expression for the solution to your equation. For a decimal approximation, use your calculator. (Note: $\"ln%2837%29%2Fln%285%29\"$ is not the same as $\"ln%2837%2F5%29\"$ !! So you have to find the two ln's separately and then divide, then subtract 3 and finally divide by 6.) \n" ); document.write( "

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