Question 1210379
<pre>

{{{log(6,(8))}}}{{{""+""}}}{{{2*log(6,(3))}}}{{{""+""}}}{{{log(6,(12))}}}{{{""-""}}}{{{log(6,(29))}}}

Use log rule:  {{{log(b,(u^n))}}}{{{""=""}}}{{{n*log(b,(u))}}}


{{{log(6,(8))}}}{{{""+""}}}{{{log(6,(3^2))}}}{{{""+""}}}{{{log(6,(12))}}}{{{""-""}}}{{{log(6,(29))}}}

<pre>

{{{log(6,(8))}}}{{{""+""}}}{{{2*log(6,(3))}}}{{{""+""}}}{{{log(6,(12))}}}{{{""-""}}}{{{log(6,(29))}}}

Use log rule:  {{{log(b,(u^n))}}}{{{""=""}}}{{{n*log(b,(u))}}}

{{{log(6,(8))}}}{{{""+""}}}{{{log(6,(3^2))}}}{{{""+""}}}{{{log(6,(12))}}}{{{""-""}}}{{{log(6,(29))}}}

{{{log(6,(8))}}}{{{""+""}}}{{{log(6,(9))}}}{{{""+""}}}{{{log(6,(12))}}}{{{""-""}}}{{{log(6,(29))}}}

Use log rule on first two terms: {{{log(b,(u))}}}{{{""+""}}}{{{log(b,(v))}}}{{{""=""}}}{{{log(b,(u*v))}}}

{{{log(6,(8*9))}}}{{{""+""}}}{{{log(6,(12))}}}{{{""-""}}}{{{log(6,(29))}}}

Use it again on the first two terms:

{{{log(6,(8*9*12))}}}{{{""-""}}}{{{log(6,(29))}}}

Use log rule: {{{log(b,(u))}}}{{{""-""}}}{{{log(b,(v))}}}{{{""=""}}}{{{log(b,(u/v))}}}

{{{log(6,((8*9*12)/29))}}}

Write {{{8=2^3}}}, {{{9=3^2}}}, {{{12=4*3=2^2*3}}}

Then {{{8*9*12}}}{{{""=""}}}{{{(2^3)*(3^2)*(2^2*3)}}}{{{""=""}}}{{{2^5*3^3}}}{{{""=""}}}{{{2^2*2^3*3^3 = (2^2*(2^3*3^3))=4*(2*3)^3 = 4*6^3}}}

So

{{{log(6,(  (8*9*12)/29  ))}}}{{{""=""}}}{{{log(6,((4*6^3)/29))}}}{{{""=""}}}
{{{log(6,(  (4/29)*6^3 ))}}}{{{""=""}}}{{{log(6,(4/29))}}}{{{""+""}}}{{{log(6,(6^3))}}}{{{""=""}}}{{{log(6,(4/29))}}}{{{""+""}}}{{{3*log(6,(6))}}}{{{""=""}}}{{{log(6,(4/29))}}}{{{""+""}}}{{{3*1}}}{{{""=""}}}{{{log(6,(4/29))}}}{{{""+""}}}{{{3}}}

Approximately 1.894382029

Edwin</pre>