Question 1066965
You have to be able to "read" the expression for a log.
{{{ f(x) = log( 2,x ) }}}
The left side says:
[ the right side of this equation is a function of {{{x}}} ]
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The 1st thing on the right side says:
[ I am a log ]
What's a log?
A log is an exponent where the base is known
So the right side is a log
What does ( 2,x ) mean?
It means:
[ the base is 2 ]
[ when 2 is raised to an exponent, the result is {{{ x }}} ]
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If I say {{{ y = f(x) }}}, then I can restate all this as:
{{{ x = 2^y }}}
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Now I write it the inverse way:
{{{ y = log( 2,x ) }}}
given:
( x,y ) = ( 2,1 )
{{{ 1 = log( 2,2 ) }}}
Read this as:
{{{ 1 }}} is the exponent and the base is {{{ 2 }}}
When {{{ 2 }}} is raised to the exponent {{{ 1 }}},
that gives me {{{ 2 }}}
Or, {{{ 2^1 = 2 }}}
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( 4,2 )
{{{ y = log( 2,x ) }}}
{{{ 2 = log( 2,4 ) }}}
{{{ 2 }}} is the exponent and the base is {{{ 2 }}}
When {{{ 2 }}} is raised to the exponent {{{ 2 }}}
that gives me {{{ 4 }}}
{{{ x = 2^y }}}
{{{ 4 = 2^2 }}}
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( 8,3 )
{{{ 3 = log( 2,8 ) }}}
{{{ 3 }}} is the exponent and the base is {{{ 2 }}}
When {{{ 2 }}} is raised to the exponent {{{ 3 }}}
that gives me {{{ 8 }}}
{{{ x = 2^y }}}
{{{ 8 = 2^3 }}}
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( 16,4 )
{{{ 4 }}} is the exponent and the base is {{{ 2 }}}
When {{{ 2 }}} is raised to the exponent {{{ 4 }}}
that gives me {{{ 16 }}}
{{{ 16 = 2^4 }}}
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Hope this helps. Practice reading log expressions.