Question

2log3-3log2 all steps I need

Answer 1

Since alogb=log(b^a)
So using this property
2log3-3log2
=log9-log8
Since loga-logb=log(a/b)
=log(9/8)

Answer 2

To Solve,

Given logarithmic equation, $2 \log 3-3 \log 2$

Here 2 log⁡3 is converted into $\log 2^{3}$ with the help of the formula which forms the basic exponential form (ie., power of) of the given logarithmic equation.  

$=\log 3^{2}-\log 2^{3} \quad\left[\text { Since, a log } b=\log b^{a}\right]$

In this step the exponential powers are calculated according to their power value and thus forms a result, = log⁡9 - log⁡8  

The above equation is of example log⁡(a) - log⁡(b)

This can be further classified into fractions of the resultant solution by using the below formula

$=\log \frac{9}{8} \quad\left[\text { since }, \log a-\log b=\log \frac{a}{b}\right]$

The solution for the given logarithmic equation is  $2 \log 3-3 \log 2=\log \frac{9}{8}$.