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 $logab=loga+logb$

$log_5 (2x)=log_5 2+log_5 x$