document.write( "Question 174943: ((log_3)s)+log_3(s-2)= 1 \n" ); document.write( "

Algebra.Com's Answer #130034 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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log_3(s) + log_3(s-2)= 1
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\n" ); document.write( "Adding logs means multiply, so we can write it:
\n" ); document.write( "log_3(s(s-2)) = 1
\n" ); document.write( ":
\n" ); document.write( "log_3(s^2-2s) = 1
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\n" ); document.write( "Write the exponent equiv:
\n" ); document.write( " $\"3%5E1\"$ = (s^2 + 2s)
\n" ); document.write( "or
\n" ); document.write( "s^2 - 2s = 3
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\n" ); document.write( "s^2 - 2s - 3 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(s-3)(s+1) = 0
\n" ); document.write( ":
\n" ); document.write( "s = -1; not a solution, s cannot be negative, (cannot have a log of a neg no.)
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\n" ); document.write( "s = 3; is the solution
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\n" ); document.write( "Check solution in original problem
\n" ); document.write( "log_3(3) + log_3(3-2)= 1
\n" ); document.write( "log base 3 of 3 = 1, log base 3 of 1 = 0, so we have:
\n" ); document.write( "1 + 0 = 1 \n" ); document.write( "

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