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Sav [38]
3 years ago
6

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

Mathematics
2 answers:
Over [174]3 years ago
6 0

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)

<em>We can use property #1 to write this as:</em>

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

<em>Now we can use property #2 to write this as:</em>

<em>Logx^{5}+Log(x+7)^{6}\\=Log((x^5)((x+7)^6)\\=Logx^{5}(x+7)^{6}</em>

<em />

<em>We see that answer choice D is right.</em>

Elina [12.6K]3 years ago
4 0

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.

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