# help appreciated, couple of maths questions watch

1. I have a couple of questions.

Consider the following formulae

y=px^2+qx+r

z=1/2 px^2+5qx

Calculate the value of x where 𝑦= 𝑧. Express the solution as an algebraic equation. Considering the following values for 𝑝= 2, q= √5, 𝑟=2.25 please provide the values of x that satisfy the previous expression 𝑦= z

and also this:

Simplify (Condense) the following [e.g. ln(x) + ln(y)= ln(xy) ]

(i) 2ln 𝑥 −3ln 𝑥+1 +ln(𝑦)

(ii) ln 4 +3ln 𝑥 −ln(𝑦+1)

(iii) ln 6𝑥 −ln 12𝑦 −3ln 𝑒

(iv) 3ln 𝑥 +3ln(𝑥−1)−3ln(𝑥2−1)

any help would be appreciated, thanks.
2. (Original post by mathless)
I have a couple of questions.

Consider the following formulae

y=px^2+qx+r

z=1/2 px^2+5qx

Calculate the value of x where 𝑦= 𝑧. Express the solution as an algebraic equation. Considering the following values for 𝑝= 2, q= √5, 𝑟=2.25 please provide the values of x that satisfy the previous expression 𝑦= z

and also this:

Simplify (Condense) the following [e.g. ln(x) + ln(y)= ln(xy) ]

(i) 2ln 𝑥 −3ln 𝑥+1 +ln(𝑦)

(ii) ln 4 +3ln 𝑥 −ln(𝑦+1)

(iii) ln 6𝑥 −ln 12𝑦 −3ln 𝑒

(iv) 3ln 𝑥 +3ln(𝑥−1)−3ln(𝑥2−1)

any help would be appreciated, thanks.
for question 1, y=z so equal them to each other, form a quadratic equation that equals 0 then use the quadratic formula? and sub in the given values?

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