Question 744927
How well do you understand what logs are?
If I say {{{ a^b = c }}}, then
{{{ a }} is the base
{{{ b }}} is the log
{{{ c }}} is the result
So I can rewrite this exactly as:
{{{ log( a,c ) = b }}}
----------------
The general rules are:
{{{ log( a,a ) = 1 }}}
{{{ log( a ) + log( b ) = log( a*b )}}}  ( the base can be 10, or anything else )
{{{ log( a^2 ) = 2*log(a) }}} ( again, the base can be anything )
----------------
{{{ log( 3,2 ) = x }}}
a)
{{{ log( 3,8 ) = log( 3, 2^3 ) }}}
{{{ log( 3, 2^3 ) = 3*log( 3,2 ) }}}
{{{ 3*log( 3,2 ) = 3x }}}
b)
{{{ log( 3,24 ) = log( 3, 3*8 ) }}}
{{{ log( 3, 3*8 ) = log( 3,3 ) + log( 3,8 ) }}}
{{{  log( 3,3 ) + log( 3,8 ) = 1 + 3x }}}
c)
{{{ log( 3, sqrt(2)) = log( 3, 2^(1/2)) }}}
{{{  log( 3, 2^(1/2)) = (1/2)*log( 3, 2 ) }}}
{{{ (1/2)*log( 3, 2 ) = x/2 }}}
d)
{{{ log( 3, 6*sqrt(2) ) = log( 3,6 ) + log( 3, sqrt(2) ) }}}
{{{ log( 3,6 ) + log( 3, sqrt(2)) = log( 3, 2*3 ) + log( 3, 2^(1/2) ) }}}
{{{  log( 3, 2*3 ) + log( 3, 2^(1/2) ) = log( 3,2 ) + log( 3,3 ) + (1/2)*log( 3,2 ) }}}
{{{ log( 3,2 ) + log( 3,3 ) + (1/2)*log( 3,2 ) = x + 1 + x/2 }}}
{{{ x + 1 + x/2 = 1 + (3x)/2 }}}