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}
15/64
Find a common factor 15 and 64 have.
15 is odd, and the only two factors 15 has is 3 and 5.
64 cannot be divided by 3 or 5.
15/64 is already simplified.
Answer:
The volume doubles to 120
Step-by-step explanation:
Volume of Rectangular Prism Formula: V = lwh
Step 1: Find volume of given lengths
V = 3(4)(5) = 60 in²
Step 2: Find volume when we double <em>h</em>
4(2) = 8
V = 3(8)(5) = 120 in²
Step 3: Divide the 2 numbers to find the ratio
120/60 = 2, or double the amount.