Log(base a)(a^4*b)-Log(base a)(a*b) is the same as
a)4
b)3
c)3a
d)a^3
I got the answer as d since subtracting logs with the same base is division. However, the answer key saids its b, Can someone please help me with this?
log(base a)(a^4*b)-log(base a)(a*b)
= log(base a)[a^4b/ab]
= log(base a) (a^3)
The power to which a has to be raised to get a^3 is 3.
That is what log(base a) a^3 means.
The answer is 3.
Ooo right, my teacher mentioned that, guessed it slipped my mind. Thanks a lot. Diploma tomorrow :(
To solve this question, we will use the logarithmic property that states:
Log(base a)(x^m) - Log(base a)(x^n) = Log(base a)((x^m)/(x^n))
In this case, we have:
Log(base a)(a^4*b) - Log(base a)(a*b)
We can simplify this expression using the property mentioned above:
= Log(base a)((a^4*b)/(a*b))
= Log(base a)(a^3)
Now, we have simplified the expression to Log(base a)(a^3).
Recall the definition of logarithm: Log(base a)(a^k) = k
Therefore, Log(base a)(a^3) equals 3, so the correct answer is option b) 3.
It seems there might have been an error in the answer key. Apologies for the confusion. The correct answer should be b) 3.