Question 954207
{{{ log(36) / log(4) }}}
{{{ log((4*9)) / log(4) }}}
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Use the rule:
{{{ log(( a*b )) = log(a) + log(b) }}}
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{{{ ( log(4) + log(9) ) / log(4) }}}
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Use the rule:
{{{ log(( a^b )) = b*log(a) }}}
{{{ ( log(( 2^2 )) + log(( 3^2 ))) / log(( 2^2 )) }}}
{{{ ( 2*log(2) + 2*log(3) ) / ( 2*log(2) ) }}}
Divide top and bottom by {{{2}}}
{{{ ( log(2) + log(3) ) / log(2) }}}
{{{ x = log(2) }}}
{{{ y = log(3) }}}
Substituting:
{{{ ( x + y ) / x }}}
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check answer:
By my calculator:
{{{ log(36) = 1.5563 }}}
{{{ log(4) = .60206 }}}
{{{ log(36) / log(4) = 1.5563 / .60206 }}} 
{{{  log(36) / log(4) = 2.5850 }}}
and
{{{ ( log(2) + log(3) ) / log(2) = ( .30103 + .47712 ) / .30103 }}}
{{{ ( log(2) + log(3) ) / log(2) = .77815 / .30103 }}}
{{{ ( log(2) + log(3) ) / log(2) = 2.5850 }}}
OK