Question

Find the value of x in the following

Answer 1

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:

‎ ‎ ‎

➝ a^m × a^n = a^(m+n)

➝ a^m / a^n = a^(m-n)

‎ ‎ ‎

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

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

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

‎ ‎ ‎

Apply division rule of exponents:

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

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

‎ ‎ ‎

Apply multiplication rule :

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

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

‎ ‎ ‎

Now since base is same, we can compare exponents

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

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

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

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

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

‎ ‎ ‎

Hence x = 2.