maths一問呀,,,log

(6+logx^3)/[log (100x)]
=(6+3log x)/(log 100+log x)
=(6+3log x)/(2+log x)
=3(2+log x)/(2+log x)
=3

6+logx^3
-------------
log (100x)

= 6+3logx ---------> (log P^M= M log P)
--------------------
log 100+ logx ---------> {log M + logN= log (MN) }

=3(2+logx) ---------> (factorization)
--------------
2+logx ---------> (log 100=2)

=3 ---------> (simplification)

6 + 3logx
= ------------------
log100 + logx


6 + 3logx
= --------------
2 + log x


3(2 + logx)
= --------------
(2 + log x)

=3