![\"\"](\"/images/stars/stars-11.gif\")
You can put this solution on YOUR website!
Solve the following logarithmic equation. Check all solutions. (Enter solutions from smallest to largest).
\n" ); document.write( "1/2log(4x+5)=log(x)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(1/2)log(4x + 5) = log(x)
\n" ); document.write( "base b when not specified is assumed to be 10
\n" ); document.write( "log(4x + 5) = 2log(x) (multiplied both sides by 2)
\n" ); document.write( "logarithmic rule: nlogb(m) = logb(m^n)
\n" ); document.write( "log(4x + 5) = log(x^2)
\n" ); document.write( "4x + 5 = x^2 (what is in parenthesis must equal)
\n" ); document.write( "-x^2 + 4x + 5 = 0
\n" ); document.write( "x^2 - 4x - 5 = 0 (divided both sides by -1)
\n" ); document.write( "(x - 5)(x + 1) = 0 by FOIL this is x^2 + x - 5x - 5 or x^2 - 4x - 5
\n" ); document.write( "x = -1 or x = 5
\n" ); document.write( "x can not be -1, 10 to the somthing can not equal - 1
\n" ); document.write( "the solution is x = 5
\n" ); document.write( "check:
\n" ); document.write( "(1/2)log(4(5) + 5) = log(5)
\n" ); document.write( "log(20 + 5) = 2log(5)
\n" ); document.write( "log(25) = log(5^2)
\n" ); document.write( "log(25) = log(25), yes
\n" ); document.write( " \n" ); document.write( "