Question

solve log(x+9)-logx=3

Answer 1

Use the following identity to solve the equation :

\(\log(a) - \log(b) = \log(\dfrac{a}{b})\)

So, you get :

\(\log(x+9) -\log(x) = 3\)
\(\implies \log(\dfrac{x+9}{x}) = 3\)

Answer 2

If the base is 10 : then

3 can be written as \(\log(10^3)\) as the power will come out : \(3 \log (10)\) and if the base is 10 , then \(\log(10) \) = 1

So, you can write it aas :

\(\log(\dfrac{x+9}{x}) = \log(10^3)\)

Answer 3

\[\log \frac{ x+9 }{ x }=3\]
\[\frac{ x+9 }{ x }=10^3=1000\]
solve for x .

Answer 4

Then follow what @surjithayer - Equate the terms inside the logarithm