Question

Condense the logarithmic expression using logarithmic properties.

3 log x + 2 log y - log y

Answer 1

Explanation:

xlog3+ylog2-ylog

log3×log2 -ylog

log6-ylog

Answer 2

Answer:
`log (x^3y )`

Explanation:

First we want to make the coefficients of the log the exponents of what is in the log

`3 log (x) + 2 log (y) - log (y)\\log (x^3) + log (y^2) - log (y)`

Now adding two log with the same base is the same as multiplying what you are taking the log of

`log (x^3) + log (y^2) - log (y)\\log (x^3y^2) - log (y)`

Now subtracting two logs with the same base is the same as dividing what you are taking the log of

`log (x^3y^2) - log (y)\\log ((x^3y^2)/(y) )`

Now we simplify

The
`y^2` cancels out the y in the denomiator

`log (x^3y^2) - log (y)\\log (x^3y )`