Question

If 81 × 125 = 3p × 5q, find p and q.

Answer 1

here is your answer:-

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Answer 2

SOLUTION

GIVEN

$\sf{81 \times 125 = {3}^{p} \times {5}^{q} }$

TO DETERMINE

The value of p and q

EVALUATION

Here the given equation is

$\sf{81 \times 125 = {3}^{p} \times {5}^{q} }$

We now solve for p and q as below

$\sf{81 \times 125 = {3}^{p} \times {5}^{q} }$

$\sf{ \implies \: {3}^{p} \times {5}^{q} =81 \times 125 }$

$\sf{ \implies \: {3}^{p} \times {5}^{q} = {3}^{4} \times {5}^{3} }$

Comparing both sides we get

p = 4 , q = 3

FINAL ANSWER

p = 4 , q = 3

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