Question

How do you condense $\ln 5-\ln x+\ln 3$ ?

Answer 1

Hint: We can solve the above given question by using the logarithmic formulae. The formulae we have to apply to solve the above given question is shown below,
Formulae should be used to solve the above given question: $\ln a+\ln b=ln\left( a\times b \right)$ and $\ln \text{a-lnb=ln}\left( \dfrac{a}{b} \right)$ . By using the above two basic formulae of logarithms we should condense the given question.

Complete step by step answer:
From the question it had been given that to condense the below equation, $\ln 5-\ln x+\ln 3$
As we have already discussed above, we have to use the above basic formulae to condense the given logarithmic equation.
First of all we have to use the formula,
$\ln a+\ln b=ln\left( a\times b \right)$
From the question it had been given that,
$\ln 5-\ln x+\ln 3$
$\Rightarrow \ln \left( 5\times 3 \right)-\ln \text{x}$
Now, we have to apply here another formula mentioned above to condense the above given question,
Now, we have to use the formula, $\ln \text{a-lnb=ln}\left( \dfrac{a}{b} \right)$
By applying the another formula we get the below equation,
$\ln \left( 15 \right)-\ln \text{x}$
$\Rightarrow \ln \left( \dfrac{15}{x} \right)$
By using the above mentioned basic formulae we get the condensed equation of the above given question,
The condensed equation we got by using the above basic formulae is, $\ln 5-\ln x+\ln 3=\ln \left( \dfrac{15}{x} \right)$
Hence the above written equation is the condensed equation.

Note:
We should be well aware of the logarithms. We should be well known about the logarithmic basic properties and basic formulae. Behind from these two there are many other logarithmic formulae which can be used in questions of this type they are given as ${{\log }_{a}}{{a}^{n}}=n$, ${{a}^{{{\log }_{a}}{{a}^{n}}}}={{a}^{n}}$ ${{\log }_{a}}a=1$ and ${{\log }_{a}}1=0$ we can use them efficiently while answering the questions.