Question

Write 2 log 3 _ 3 log 2 as log N

Answer 1

Answer:

$log(\frac{9}{8})$

Step-by-step explanation:

2log3-3log2

=$log 3^2-log 2^3$

=$log(\frac{3^2}{2^3})$

=$log(\frac{9}{8})$

where N=$\frac{9}{8}$

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Answer 2

Given:

2 log 3 _ 3 log 2

To Find:

convert expression into log N

Step-by-step explanation:

• Here we will use the concept of Logarithms to reduce the expression to log N.
• $log(a)-log(b)=log(a/b)\\log(a)+log(b)=log(ab)\\mlog(a)=log(a^{m} )$we will use these properties to solve the expression and then reduce it to the simple expression .
• Firstly we can write $2log(3)$ as $log(3^{2})=log(9)$ and then similarly we can write $3log(2)$ as $log(2^{3} )=log(8)$ .
• Now we have the expression that reduces to $log9-log8$ and now we will again use the property to reduce this expression to $log(9/8)$.
• Here we only use the identities to reduce the expression again and again  and we have log N as log(9/8) so here N=9/8.

The answer is log(9/8)