Question

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

Answer 1

Answer: option d.

Step-by-step explanation:

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

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

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.

Answer 2

Answer:

D

Step-by-step 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.