document.write( "Question 1203185: 6 logx 25 = 7 - log5 x
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Algebra.Com's Answer #838550 by greenestamps(13209) $\"\"$ $\"About$

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\n" ); document.write( "To avoid having to type all those log expressions....

\n" ); document.write( "Define $\"y=log%28x%2C5%29\"$

\n" ); document.write( "The given equation is

\n" ); document.write( " $\"6log%28x%2C25%29=7-log%285%2Cx%29\"$

\n" ); document.write( "Note $\"log%28x%2C25%29=log%28x%2C5%5E2%29=2log%28x%2C5%29\"$ and $\"log%285%2Cx%29=1%2Flog%28x%2C5%29\"$

\n" ); document.write( "Then the equation is

\n" ); document.write( " $\"6%282y%29=7-1%2Fy\"$
\n" ); document.write( " $\"12y=7-1%2Fy\"$
\n" ); document.write( " $\"12y%5E2=7y-1\"$
\n" ); document.write( " $\"12y%5E2-7y%2B1=0\"$
\n" ); document.write( " $\"%284y-1%29%283y-1%29=0\"$

\n" ); document.write( "The possible solutions are $\"y=1%2F4\"$ and $\"y=1%2F3\"$ .

\n" ); document.write( " $\"y=1%2F4\"$ --> $\"log%28x%2C5%29=1%2F4\"$ --> $\"x%5E%281%2F4%29=5\"$ --> $\"x=5%5E4=625\"$

\n" ); document.write( " $\"y=1%2F3\"$ --> $\"log%28x%2C5%29=1%2F3\"$ --> $\"x%5E%281%2F3%29=5\"$ --> $\"x=5%5E3=125\"$

\n" ); document.write( "ANSWERS: x=125 and x=625

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