A)
to solve a, the following rules are crucial:
(i)
so the difference of 2 logarithms with the same base, is the logarithm of their division, preserving the same base.
(ii) if
then b=c.
so if 2 logarithms with the same base are equal, then the arguments (b and c) are equal as well.
so
apply rule (i):
apply rule (ii):
now 'isolate' y:
b)
some more rules:
(iii)
(iv)
apply iii and iv:
then substitute
in the equation:
so now we have a quadratic equation of degree 2,
a=2, b=-5, c=2
the discriminant is
, the root of it is 3
so the roots are:
and
finally, we convert u's to x's:
means
so for u=2, x=4, and for u=1/2 we have x=1/4
Answers:
A) y=(6 x^{2} -1) \frac{(x-1)}{x}
B) solution set: {4, 1/4}
Answer: D
Step-by-step explanation:
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
Answer:
Pyramid
Step-by-step explanation:I just is
-8———————0——————————10
-7 7
That’s -7 and 7 on a number line. If you count the — each is one so that is where they would be if you plotted the number line.
To check if x = 9 is the solution, we need to replace every x with 9 and simplify
(3+x)/4 = 3
(3+9)/4 = 3
12/4 = 3
3 = 3
We get the same thing on both sides, so the last equation is a true equation. This means that the first equation is a true equation when x = 9. Therefore, the solution x = 9 is confirmed.