Question 1060994
Here's the trick:
You already said {{{ log( 25,5 ) = 1/2 }}}
Take the reverse of this and plug it into
your 2nd equation:
{{{ log( 25,x ) + log( 25,( x^2 - 1 ) ) - log( 25, x+1 ) - 1/2 }}}
{{{ log( 25,x ) + log( 25,( x^2 - 1 ) ) - log( 25, x+1 ) - log( 25,5 ) }}}
Now use the rules:
{{{ log( a,b ) + log( a,c ) = log( a, b*c ) }}}
{{{ log( a,b ) - log( a,c ) = log( a, b/c ) }}}
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{{{ log( 25, ( x^2 - 1 ) / ( x+1 ) ) + log( 25, x/5 ) }}}
{{{ log( 25, x - 1 ) + log( 25, x/5 ) }}}
{{{ log( 25, ( x^2 - x )/5 ) }}}
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check the answer:
In the original equation, I'll say {{{ x = 24 }}},
because numbers work out good
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{{{ log( 25,x ) + log( 25,( x^2 - 1 ) ) - log( 25, x+1 ) - 1/2 }}}
{{{ log( 25,24 ) + log( 25,( 24^2 - 1 ) ) - log( 25, 24+1 ) - 1/2 }}}
{{{ log( 25,24 ) + log( 25, 23*25 )  - 1 - 1/2 }}}
{{{ log( 25,24 ) + 1 + log( 25,23 ) - 3/2 }}}
{{{ log( 25, (23*24) ) - 1/2 }}}
{{{ log( 25, (552) ) - 1/2 }}}
It can also be:
{{{ log( 25, 552/5 ) }}}
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Now I'll check the answer:
{{{ log( 25, ( x^2 - x )/5 ) }}}
{{{ log( 25, ( 24^2 - 24 )/5 ) }}}
{{{ log( 25, ( 576 - 24 )) - 1/2 }}}
{{{ log( 25, (552) ) - 1/2 }}}
OK
Hope I got it!