Simplify the following?

Question

Ques (1) #log_10 (10^6)-log_10 (10^9)#
Ques (2) #log_5 (2x)#

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Answer 1 · 2017-05-23T13:39:57

Ques.(1) #log_10 (10^6)-log_10 (10^9)=-3#
Ques.(2) #log_5 (2x)=log_5 2+log_5 x#

Ques.(1)

As #log_10 10=1# and #log_10 (10^n)=nlog_10 10=nxx1=n#

#log_10 (10^6)-log_10 (10^9)#

= #6-9#

= #-3#

Ques.(2)

As #logab=loga+logb#

#log_5 (2x)=log_5 2+log_5 x#