Question

how to solve the log expression

Answer 1

Please send the question clearly.

Answer 2

Answer:

Given: Logarithmic Expression = - log$(10^{-8}+10^{-7})$

Following are the steps:--

To solve given Expression we first change negative exponent to positive exponent

⇒ -  log($\frac{1}{10^{8}}+\frac{1}{10^{7}})$

Now, we add the rational no by making same denominator

⇒ -  log$(\frac{1}{10^{8}}+\frac{10}{10^{8}})$

⇒ -  log$(\frac{11}{10^{8}})$

Now, Using logarithmic law, $log(\frac{m}{n})=log\,m - log\,n$ we get,

⇒ - ( log ( 11 ) - log($10^{8}$)  )

Now using another logarithmic law, $log \,m^n =log\, n\times log\,m$

⇒ - ( log ( 11 ) - 8 × log 10 )  

now using distributive property,

⇒ - log 11 + 8 × log 10  

⇒ 8 - log 11  ( ∵ value of log 10 = 1 )

Therefore, - log[$10^{-8}+10^{-7}$] = 8 - log 11