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If x^3x = (3x)^4x, then find the value of x.
\n" ); document.write( "There's a lot going on here. Firs, let's use an exponent rule:
\n" ); document.write( "x^3x = (x^3)^x and
\n" ); document.write( "(3x)^4x = ((3x)^4)^x
\n" ); document.write( "So we have:
\n" ); document.write( "(x^3)^x = ((3x)^4)^x
\n" ); document.write( "Take the log of both sides (remembering log rules):
\n" ); document.write( "x log x^3 = x log (3x)^4 ( log rules - email for more info on this if it doesn't make sense)
\n" ); document.write( "Divide both sides by x log:
\n" ); document.write( "x^3 = (3x)^4
\n" ); document.write( "x^3 = (3^4)(x^4) (more exponent rules)
\n" ); document.write( "x^3 = (81)(x^4)
\n" ); document.write( "(x^3)/(x^4) = 81 (divided both sides by x^4)
\n" ); document.write( "1/x = 81 (even more exponent rules)
\n" ); document.write( "x = 1/81 \n" ); document.write( "