Question

if 7^x-2+2352=7^x. Find the value of x.​

Answer 1

Answer:x=4

Step-by-step explanation

Answer 2

Question :

Find the value of x .If

$\sf7 {}^{x - 2} + 2352 = 7 {}^{x}$

Solution :

$\sf7 {}^{x - 2} + 2352 = 7 {}^{x}$

$\sf \implies 7 {}^{x} \times 7 {}^{ - 2} + 2352 = 7 {}^{x}$

Let $\sf7 {}^{x} = y$

$\sf \implies \: y \times \dfrac{1}{49} + 2352 = y$

$\sf \implies \dfrac{y + 2352 \times 49}{49} = y$

$\sf \implies \: y + 115248 = 49y$

$\sf \implies48y = 115248$

$\sf \implies \: y = \cancel{ \frac{115248}{48}} = 2401$

$\sf \implies \: 7 {}^{x} = 2401$

$\sf \implies \: 7 {}^{x} = 7 {}^{4}$

On camparing x = 4

Therefore, the value of x= 4

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Exponents formula's :

$\sf1)y {}^{m} \times y {}^{n} = y {}^{m + n}$

$\sf2) \dfrac{y {}^{m} }{y {}^{n} } = y {}^{m - n}$

$\sf3)y {}^{0} = 1$