Question

Write ln 2x + 2x ln x -ln 3y as a single logarithm.

Answer 1

Answer: option c.

Step-by-step explanation:

 To solve this problem you must keep on mind the properties of logarithms:

$ln(b)-ln(a)=ln(\frac{b}{a})\\\\ln(b)+ln(a)=ln(ba)\\\\a*ln(b)=ln(b)^a$

Therefore, knowing the properties, you can write the expression gven in the problem as shown below:

$ln2x+2lnx-ln3y=ln2x+lnx^2-ln3y\\\\=ln(2x)(x^2)-ln3y\\\\=ln(\frac{2x^3}{3y})$

Therefore, the answer is the option c.

Answer 2

Answer:

C

Step-by-step explanation:

We can use 3 properties here to write this as single logarithm:

1. Log (a^b) = b Log a

2. Log x + Log y = Log (x*y)

3. Log x - Log y = Log (x/y)

We can use property #1 first to write:

$ln2x+2lnx-ln3y\\=ln2x+lnx^2-ln3y$

Now we can use property #2 and property #3 to write this as single logarithm:

$ln2x+lnx^2-ln3y\\=ln(\frac{(2x)(x^2)}{3y})\\=ln(\frac{2x^3}{3y})$

Answer choice C is right.