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Question
3 ln (x + 7) - 4 ln (x^2 + 7)
When 4•ln(3) is seen, it is the same as ln(3^4).
This said, 3•ln(x+7) is the same as ln((x+7)^3).
Also, -4ln(x²+7) is the same as ln((x+7)^-4) = ln(1/(x+7)^4).
Now the equation can be rewritten as ln((x+7)^3) - ln(1/(x+7)^4).
Now when you have -ln(1/a), it is the same as ln(a).
In this way, - ln(1/(x+7)^4) is the same as + ln((x+7)^4).
Now we have ln((x+7)^3) + ln((x+7)^4).
It is also known that ln(a)•ln(b) = ln(ab), so we can say that
ln((x+7)^3) + ln((x+7)^4) = ln((x+7)^3•(x+7)^4).
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