Question

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

Answer 1

C

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(((2x)(x^2))/(3y))\\=ln((2x^3)/(3y))`

Answer choice C is right.

Answer 2

Answer: option c.

Explanation:

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

`ln(b)-ln(a)=ln((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((2x^3)/(3y))`

Therefore, the answer is the option c.