Question

p= (50y^2)^3÷81x^3 then prove that logp+3logx-6logy=6-3log2-4log3​

Answer 1

Answer:

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

(3 • (a3)) - 34x3

STEP

2

:

Equation at the end of step

2

:

3a3 - 34x3

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

3a3 - 81x3 = 3 • (a3 - 27x3)

Trying to factor as a Difference of Cubes:

4.2 Factoring: a3 - 27x3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0-b3 =

a3-b3

Check : 27 is the cube of 3

Check : a3 is the cube of a1

Check : x3 is the cube of x1

Factorization is :

(a - 3x) • (a2 + 3ax + 9x2)

Trying to factor a multi variable polynomial :

4.3 Factoring a2 + 3ax + 9x2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

3 • (a - 3x) • (a2 + 3ax + 9x2)