Answer: (2*p + 3)/q
Step-by-step explanation:
First, let's remember the relationships:
Logₙ(a) = Ln(a)/Ln(n)
Ln(A*B) = Ln(A) + Ln(B)
Ln(a^n) = n*Ln(a)
Now, we know that:
Logₓ(2) = p
Logₓ(7) = q
We want to express:
Log₇(4*x^3) in terms of p and q.
First, we can rewrite the first two relations as:
Ln(2)/Ln(x) = p
Ln(7)/ln(x) = q
then we have:
Ln(2) = p*Ln(x)
Ln(7) = q*Ln(x)
Ok:
Now let's play with our equation:
Log₇(4*x^3)
First, this is equal to:
Ln(4*x^3)/Ln(7)
We now can rewrite this as:
(Ln(4) + Ln(x^3))/Ln(7)
= (Ln(2^2) + Ln(x^3))/Ln(7)
= (2*Ln(2) + 3*Ln(x))/Ln(7)
Now we can replace Ln(2) by p*Ln(x) and Ln(7) by q*Ln(x)
(2*p*Ln(x) + 3*Ln(x))/(q*Ln(x)) = (2*p + 3)/q
This is the expression we wanted.
Y= (x-1) /3 is the correct answer
I’m assuming that -0.7 was multiplied with -1/2
4. B is the answer
5. A is the answer ( y is the same , x are the opposite)
6. C
7. D
Answer:
2/3
Step-by-step explanation:
log27(9)
Factor the number: 27=3³
= log3³(9)
Apply log rule: loga^b(x) - 1/b loga(x).
log3³(9) =1/3 log3³(9)
=1/3 log3³(9)
Factor the number: 9=3²
=1/3 log3³(3²)
Apply log rule: loga(a^b) =b
log3 (3²) =2
1/3×2
=2/3
