Question

Find the x
Thank you

Answer 1

Answer:

$\frac{ {5}^{3x} \times 25}{ {5}^{x} } = {5}^{3} \times 125 \\ \\ = >$

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Step-by-step explanation:

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Answer 2

Answer:

• x = 2

Step-by-step explanation:

In the given question, we have to find the value of x. To solve this problem, we will apply the exponential rule according to which:

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➝ a^m × a^n = a^(m+n)

➝ a^m / a^n = a^(m-n)

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$\sf : \implies \dfrac{5^{3x} \times 25}{5^{x} } = {5}^{3} \times 125$

$\sf : \implies \dfrac{5^{3x} \times (5 \times 5) }{5^{x} } = {5}^{3} \times (5 \times 5 \times 5)$

$\sf : \implies \dfrac{5^{3x} \times 5 ^{2} }{5^{x} } = {5}^{3} \times5 ^{3}$

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Apply division rule of exponents:

$\sf : \implies {5^{3x - x} \times 5 ^{2} } = {5}^{3} \times5 ^{3}$

$\sf : \implies {5^{2x} \times 5 ^{2} } = {5}^{3} \times5 ^{3}$

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Apply multiplication rule :

$\sf : \implies {5^{2x + 2} } = 5 ^{3 + 3}$

$\sf : \implies {5^{2x + 2} } = 5 ^{6}$

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Now since base is same, we can compare exponents

$\sf : \implies {2x + 2} ={6}$

$\sf : \implies {2x } ={6 - 2}$

$\sf : \implies {2x } ={4}$

$\sf : \implies {x } = \dfrac{4}2$

$\large\pink{ \boxed{ \sf : \implies {x } = 2}}$

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Hence x = 2.