Question

solve 2+1/2log10^9-2log10^5​

Answer 1

Answer:

-9/2

Step-by-step explanation:

$\implies 2 + \dfrac{1}{2}\:\:log\:10^9 - 2\:\:log\:10^5$

According to property of Logarithms,

⇒ Log aⁿ = n . Log a

E.g. Log 10³ = 3 × Log 10 = 3 × 1 = 3

Coming to your question, we see that Log 10⁹ can be written as:

9 × Log 10 = 9 × 1 = 9

Similarly, Log 10⁵ = 5 × Log 10 = 5 × 1 = 5

Substituting these in the question we get,

⇒ 2 + 1/2 ( 9 ) - 2 ( 5 )

⇒ 2 + 4.5 - 10

⇒ 6.5 - 10

⇒ -4.5 or -9/2

Hence -9/2 is the required answer.

Hope it helped !!