document.write( "Question 30319: How do you solve a log equations where there is x on both sides and one where there is only one x on one side? Such as the following?\r
\n" ); document.write( "\n" ); document.write( " $\"+log+%28+3%2C+x+%29%5E2\"$ = $\"+log%28+3%2C+4+%29\"$
\n" ); document.write( "&\r
\n" ); document.write( "\n" ); document.write( " $\"+log+%282%2C+%28x%2B2%29%29%5E2\"$ = $\"log+%282%2C%283x%2B16%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Thank you very much!!! \n" ); document.write( "

Algebra.Com's Answer #16982 by sdmmadam@yahoo.com(530) $\"\"$ $\"About$

You can put this solution on YOUR website!
log ( 3, x )^2 =log( 3, 4 )\r
\n" ); document.write( "\n" ); document.write( "log(base 3)(x^2) = log(base 3)(4) implies
\n" ); document.write( "(x^2) = 4
\n" ); document.write( "(using log p = log q implies p = q of course when the base is the same )
\n" ); document.write( "(x^2) = 2^2
\n" ); document.write( "x = 2 (when the powers are the same the base are equal)
\n" ); document.write( "Answer:x = 2
\n" ); document.write( "Verification: x = 2 holds.
\n" ); document.write( "even oral checking is enough\r
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\n" ); document.write( "\n" ); document.write( "log (2, (x+2))^2}}} = log (2,(3x+16))
\n" ); document.write( "log (x+2)^2 = log (3x+16) (for the same base 2)----(1)
\n" ); document.write( "which implies (x+2)^2 = (3x+16)
\n" ); document.write( "(using log p = log q implies p = q of course when the base is the same )
\n" ); document.write( "That is x^2+4x+4 = 3x+16
\n" ); document.write( "x^2+(4x-3x)+(4-16)= 0 (grouping like terms)
\n" ); document.write( "x^2+(4x-3x)-12= 0 (the product is (-12) and the difference is 1)
\n" ); document.write( "x^2+4x-3x-12= 0
\n" ); document.write( "x(x+4)-3(x+4) = 0
\n" ); document.write( "xp-3p =0 where p= (x+4)
\n" ); document.write( "p(x-3) =0
\n" ); document.write( "(x+4)(x-3) =0
\n" ); document.write( "(x+4) =0 implies x = -4
\n" ); document.write( "(x-3) =0 implies x = 3
\n" ); document.write( "Verification: x =-4 in (1) gives
\n" ); document.write( "LHS = log (x+2)^2 = log(-4+2)^2 = log(-2)^2 = log 4 (for the base 2)
\n" ); document.write( "RHS = log(3x+16) = log[3X(-4)+16]= log(-12+16) = log 4 (for the base 2) = LHS\r
\n" ); document.write( "\n" ); document.write( "Verification: x = 3 in (1) gives
\n" ); document.write( "LHS = log (x+2)^2 = log(3+2)^2 = log(5)^2 = log 25 (for the base 2)
\n" ); document.write( "RHS = log(3x+16) = log[3X3+16]= log(9+16) = log 25(for the base 2) = LHS
\n" ); document.write( "Therefore our values are correct.\r
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