Question

Which is log x+ 6 log(x+7) written as a single logarithm.

Answer 1

D

Explanation:

We can use 2 properties of logs to write this as single logarithm:

1.
`Log(A^B)=BLog A`

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

We can use property #1 to write this as:

`5Logx+6Log(x+7)\\=Logx^(5)+Log(x+7)^(6)`

Now we can use property #2 to write this as:

`Logx^(5)+Log(x+7)^(6)\\=Log((x^5)((x+7)^6)\\=Logx^(5)(x+7)^(6)`

We see that answer choice D is right.

Answer 2

Answer: option d.

Explanation:

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

`log(b)-log(a)=log((b)/(a))\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a`

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

`5logx+6log(x+7)=logx^5+log(x+7)^6=logx^5(x+7)^6`

Then, the answer is the option d.