The answer to the equation is 8
Answer: 
is the logarithmic equation which is equivalent to
.
Step-by-step explanation:
According to the laws of logarithms
,where b=base ,n,x all are positive
It can be written in exponential form such as
Now in the given question x=9 ,b=3 and n=2 such that it will equals to
Hence the logarithmic equation for is.
Answer:
85
Step-by-step explanation:
0.350 L × n = 30 L . . . . . where n is the number of bottles.
Divide by 0.350:
n = (30 L)/(0.350 L) ≈ 85.7
85 bottles can be filled, and one can be partially filled.
_____
Of course, you know the SI prefix milli- means 1/1000, so 350 mL = 350/1000 L = 0.350 L. When you do the division indicated above, ...
(30 L)/(0.350 L)
the units of liters cancel, and you are left with the number of bottles.
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
