There's a property of logs I want you to remember, that is:
log(a)ᵇ = b*log(a)
We'll be using this property to solve the question
<u>Finding x:</u>
log(2)ˣ = log(3)
x*log(2) = log(3) [using the property mentioned above]
x = log(3) / log(2) [dividing both sides by log(2)]
Hence, the correct answer is option E.
Answer:
c = 6
Step-by-step explanation:
The compound inequality is c < x < 5
If we want a value of c such that there are no solutions, we need to make that inequality false.
From the inequality we can see that 5 must be greater than c to be true.
Therefore, we need to choose a value smaller or equal than 5.
For example, c=6.
If c = 6, that means that x is greater than 6 and smaller than 5. That's impossible, there is no number that meets that.
Therefore, our compound inequality 6 < x < 5 has no solutions.
The given set of equations:
y=-3x+1............(1)
y=2x-4 .............(2)
can be solved most conveniently by rewriting as
y =-3x+1 = 2x-4
We concentrate on the right equality, which is expressed in x only:
-3x+1 = 2x-4
Transpose and solve for x
1+4 = 2x+3x
5x=5
x=5/5=1
Substitute x=1 in the
first equation: y=-3(1)+1=-2
second equation: y=2*x-4=2(1)-4=-2
So the solution is x=1, y=-2, or (1,-2)