Condense the logarithmic expression using logarithmic properties. 3 log x + 2 log y - log y

Question

asked Oct 12, 2023 234k views

2 Answers

Shardae · Answer 1 · 2023-10-16T12:42:14+0000

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

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