document.write( "Question 501109: 1. There is one x satisfying 5^(−3x−2)=1/78125. Use the rules of exponentiation and logarithms to find this number.\r
\n" ); document.write( "\n" ); document.write( "The value of x is...\r
\n" ); document.write( "\n" ); document.write( "2. There is one x satisfying log3(4x−8)=1. Use the rules of exponentiation and logarithms to find this number.\r
\n" ); document.write( "\n" ); document.write( "The value of x is... \n" ); document.write( "
Algebra.Com's Answer #338439 by lwsshak3(11628)\"\" \"About 
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1. There is one x satisfying 5^(−3x−2)=1/78125. Use the rules of exponentiation and logarithms to find this number.
\n" ); document.write( "The value of x is...
\n" ); document.write( "2. There is one x satisfying log3(4x−8)=1. Use the rules of exponentiation and logarithms to find this number.
\n" ); document.write( "The value of x is..
\n" ); document.write( "**
\n" ); document.write( "1. 5^(−3x−2)=1/78125=78125^-1
\n" ); document.write( "Take log of both sides
\n" ); document.write( "(-3x-2)log 5=(-1) log 78125
\n" ); document.write( "(-3x-2)/(-1)=- log 78125/log 5
\n" ); document.write( "3x+2=-7
\n" ); document.write( "3x=-9
\n" ); document.write( "x=-3
\n" ); document.write( "Check:
\n" ); document.write( "5^(−3x−2)=5^-7=12.8*10^-6
\n" ); document.write( "1/78125=78125^-1=12.8*10^-6
\n" ); document.write( "..
\n" ); document.write( "2. log3(4x−8)=1
\n" ); document.write( "convert to exponential form: base(3) raised to log of number(1)=number(4x-8)
\n" ); document.write( "3^1=4x-8
\n" ); document.write( "3=4x-8
\n" ); document.write( "4x=11
\n" ); document.write( "x=11/4
\n" ); document.write( "Check:
\n" ); document.write( "log3(4x-8)=log(11-8)=log3(3)=1 (log of any base to its base=1) \n" ); document.write( "
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