Question 1050952
{{{ 2*log( 5, (1/25) ) }}}
I can make an equation out of this
{{{ x = 2*log( 5, (1/25) ) }}}
{{{ x/2 = log( 5, (1/25) ) }}}
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This says that {{{ x/2 }}} is a log ( exponent ), and
when {{{ 5 }}} is used as a base for this log, the
result is {{{ 1/25 }}}
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So, I can rewrite this as:
{{{ 5^(x/2) = 1/25 }}}
{{{ 5^(x/2) = 1/((5^2)) }}}
{{{ 5^(x/2) = 5^(-2) }}}
{{{ x/2 = -2 }}}
{{{ x = -4 }}} answer
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check answer:
{{{ x = 2*log( 5, (1/25) ) }}}
{{{ -4 = 2*log( 5, (1/25) ) }}}
{{{ -2 = log( 5,(1/25) ) }}}
{{{ -2 = log( 5, .04 ) }}}
{{{ 5^(-2) = .04 }}}
{{{ .04 = .04 }}}
OK ( used my calculator to check )