Question

How do you condense $ \ln x+\ln 3 $ ?

Answer 1

Hint: We solve the given equation using the particular identity formula of logarithm like $ \ln a+\ln b=\ln \left( ab \right) $ . The main step would be to eliminate two logarithm functions and keep it as a single logarithm. we solve the linear multiplication with the help of basic binary operations.

Complete step by step answer:
We take the logarithmic identity for the given equation $ \ln x+\ln 3 $ to find the solution for condensation.
For the condensed form of the logarithm, we apply power property, products of factors, and the logarithm of a power.
For our given equation we are only going to apply the product property.
$\Rightarrow$ We have $ \ln a+\ln b=\ln \left( ab \right) $ .
In the case of logarithmic addition of the terms $ a $ and $ b $, we have to multiply the terms to get the single logarithmic function.
Now we place the values of $ a=x $ and $ b=3 $ in the equation of $ \ln a+\ln b=\ln \left( ab \right) $ .
$\Rightarrow$ We get $ \ln x+\ln 3=\ln \left( 3x \right) $ .
Therefore, the condensed form of $ \ln x+\ln 3 $ is $ \ln 3x $ .

Note:
 There are some particular rules that we follow in case of finding the condensed form of the logarithm. We first apply the power property first. Then we identify terms that are products of factors and a logarithm and rewrite each as the logarithm of a power. Then we apply the product property. Rewrite sums of logarithms as the logarithm of a product. We also have the quotient property rules.