Question 1074154
{{{ 2 - log( 2x ) = log( x/18 ) }}}
Convert {{{ 2 }}} to a base 10 log
{{{ 2 = log( 100 ) }}}
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{{{ log( 100 ) - log( 2x ) = log( x/18 ) }}}
{{{ log( 100/(2x)) = log( x/18 ) }}}
{{{ 100/(2x) = x/18 }}}
{{{ 50/x = x/18 }}}
{{{ 50*18 = x^2 }}}
{{{ x^2 = 900 }}}
{{{ x = 30 }}}
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Only the positive square root is allowed since
any log with base 10 cannot result in a negative number
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check answer:
{{{ log( 100 ) - log( 2x ) = log( x/18 ) }}}
{{{ log( 100 ) - log( 2*30 ) = log( 30/18 ) }}}
{{{ log( 100 ) - log( 60 ) = log( 5/3 ) }}}
{{{ log( 100 ) - log( 60 ) = log( 5 ) - log( 3 ) }}}
{{{ 2 - 1.77815 = .69897 - .477121 }}}
{{{ .22185 = .221849 }}}
close enough