Question 735892
If the equation {{{ y=2^x }}} is graphed, which of the following values of x would produce a point closest to the x-axis? A.{{{ 1/4 }}} B. {{{ 3/4 }}} C. {{{ 5/3 }}} D. {{{ 8/3 }}}


{{{ y=2^x }}}....plug in given values


{{{ y=2^x }}}.....for {{{ 1/4 }}}


{{{ y=2^(1/4) }}}

{{{ y=root(4,2) }}}

{{{ highlight(y=1.19) }}}


{{{ y=2^x }}}.....for {{{ 3/4 }}}


{{{ y=2^(3/4) }}}

{{{ y=root(4,2^3) }}}

{{{ y=root(4,8) }}}

{{{ highlight(y=1.68) }}}


{{{ y=2^x }}}.....for {{{ 5/3 }}}


{{{ y=2^(5/3) }}}

{{{ y=root(3,2^5) }}}

{{{ highlight(y=3.18) }}}



{{{ y=2^x }}}.....for {{{8/3 }}}


{{{ y=2^(8/3) }}}

{{{ y=root(3,2^8) }}}

{{{ y=root(3,256) }}}

{{{ highlight(y=6.35) }}}

so, a point closest to the x-axis would be for A.{{{ 1/4 }}}: ({{{ 1/4 }}},{{{ 1.19 }}})


see it on a graph:


{{{ drawing( 600, 600, -10, 10, -10, 10,circle(1/4,1.1892,0.2),circle(3/4,1.68,0.2),circle(5/3,3.18,0.2),circle(8/3,6.3496 ,0.2),
graph( 600, 600, -10, 10, -10,10,2^x)) }}} 


2.
let the value of {{{ log( 3, 27) }}} be {{{x}}}

we are actually looking for {{{x^3=27}}} ...solve for {{{x}}} 

{{{x=root(3,27)}}}

{{{x=root(3,3^3)}}}

{{{x=3}}}

so, {{{ log( 3, 27)=3 }}}