document.write( "Question 946643: Solve fora in log(2a)- 3log2= 1/2log(a-3) \n" ); document.write( "

Algebra.Com's Answer #854615 by ikleyn(53937) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Solve for a in log(2a)- 3log2= 1/2log(a-3).
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        @lwsshar3 in his post gives the answer \"no real solutions\".\r
\n" ); document.write( "\n" ); document.write( "        This answer is incorrect.\r
\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "log(2a)- 3log2 = 1/2*log(a-3)
\n" ); document.write( "log(2a/(2^3)) = log((a-3)^(1/2))
\n" ); document.write( "2a/8 = (a-3)^(1/2)
\n" ); document.write( "a/4 = sqrt(a-3)
\n" ); document.write( "a = 4*sqrt(a-3)
\n" ); document.write( "square both sides:
\n" ); document.write( "a^2 = 16*(a-3)
\n" ); document.write( "a^2 = 16a - 48
\n" ); document.write( "a^2 - 16a + 48 = 0
\n" ); document.write( "Discriminant d = b^2-4ac = (-16)^2 - 4*16*48 = 64\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"a%5B1%2C2%5D\"$ = $\"%2816+%2B-+sqrt%2864%29%29%2F2\"$ = $\"%2816+%2B-+8%29%2F2\"$         (quadratic formula)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The solutions are a = 12 and a = 4.        ANSWER\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Both solutions satisfy the original equation.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );