Question 925847
When the base is not shown, the base is
normally {{{ 10 }}}, because there has to
be some base
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{{{ log( 5x ) = log(3) + log(( x-2 )) }}}
use the following general rule on the right side:
{{{ log( a ) + log( b ) = log( a*b ) }}}
{{{ log( 5x ) = log(( 3*( x - 2 ))) }}}
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The next step can be stated as:
If the logs of 2 expressions are 
equal, then the result of raising 
the bases to those logs are equal, so
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{{{ 5x = 3*( x-2 ) }}}
{{{ 5x = 3x - 6 }}}
{{{ 2x = -6 }}}
{{{ x = -3 }}}
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check the answer:
{{{ log( 5x ) = log(3) + log(( x-2 )) }}}
{{{ log(( 5*(-3) )) = log(3) + log(( -3-2 )) }}}
{{{ log(( -15 )) = log(( 3*(-5) )) }}}
{{{ -15 = -15 }}}
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There is a problem with this, and you should get 
more opinions on it. You can't possible get a
negative result by raising {{{ 10 }}} ( or any (+) base )
to any log. This seems to be what is happening.
What's the deep explanation, or is this a bogus
problem? Try to get an answer.