Question 742270
,{{{ log( 9, 1/27 ) }}} , {{{ log ( 9, sqrt( 3 ) )}}}, {{{ log ( 8, root( 3, 2 ))}}}, and {{{ log ( 3, root( 3, 1/9 ))}}}
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exponential form: base(b) raised to log of the number(k)=number(N)
using x in place of k
..
{{{ log( 9, 1/27 ) }}}
9^x=1/27
3^2^x=1/3^3
3^2x=3^-3
2x=-3
x=-3/2
{{{log(9,(1/27))=-3/2}}}
..
{{{ log ( 9, sqrt( 3 ) )}}}
9^x=3^(1/2)
3^2x=3^(1/2)
2x=1/2
x=1/4
{{{ log ( 9, sqrt( 3 ))=1/4}}}
..
{{{ log ( 8, root( 3, 2 ))}}}
8^x=2^(1/3)
2^3x=2^(1/3)
3x=1/3
x=1/9
{{{ log ( 8, root( 3, 2 ))=1/9}}}
..
{{{ log ( 3, root( 3, 1/9 ))}}}
3^x=(1/9)^(1/3)
3^x=(3^-2)^(1/3)
3^x=3^(-2/3)
x=-2/3
{{{ log ( 3, root( 3, 1/9 ))=-2/3}}}