Use the rules of logarithm:
1. log(x)+log(y)=log(xy)
log(x)-log(y)=log(x/y)
2. k*log(x) = log(x^k)
log(x)/k = log(x^(1/k))
<span>log(2z)+2log(2x)+4log(9y)+12log(9x)−2log(2y)
=</span>log(2z)+log(4x^2)+log(9^4y^4)+log(9^12x^12)−log(4y^2)
=log(2z)+log(4x^2)+log(6561y^4)+log(282429536481x^12)−log(4y^2)
=log(59296646043258912 * x^14 * y^6 * z)
Answer: the system of equations are
x + y = 35
3x + 2y = 100
Step-by-step explanation:
Let x= the number of short answer questions.
Let y= the number of multiple choice questions.
Noah wants 35 questions on the exam. This means that
x + y = 35
He plans to mix short answer questions, worth 3 points, with multiple choice questions worth 2 points. This means that x short answer questions will give 3x points and y multiple choice questions will give 2y points
Since the exam is worth 100 points, then,
3x + 2y = 100 - - - - - - - -1
Substituting x = 35 - y into equation 1, it becomes
3(35 - y) + 2y = 100
105 - 3y + 2y = 100
y = 105 - 100 = 5
x = 35 - y = 35 - 5
x = 30
The expressions is undefined in the set of the real numbers.