Question

Find y,
4^y x 4^3 = 4^12

Find r,
3^7 x 3^r = 3^4

Find k
5^k = 1/25

Answer 1

Check the picture you will find the answer

Answer 2

Question 1 :

$\bf Find \: y,$

$\bf 4^y \times 4^3 = 4^{12}$

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Solution :

$\bf 4^y \times 4^3 = 4^{12}$

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$\pink{\bf Now, \: we \: know \: that \: a^m \times a^n = a^{m+n}}$

$\bf \implies 4^{y + 3} = 4^{12}$

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Now, on both sides bases are same,

Therefore, powers will be equal

$\bf \implies y + 3 = 12$

$\bf \implies y = 12 - 3$

$\bf \implies y = 9$

$\large \boxed{\bf y = 9}$

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Question 2 :

$\bf Find \: r,$

$\bf 3^7 \times 3^r = 3^4$

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Solution :

$\bf 3^7 \times 3^r = 3^4$

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$\pink{\bf Now, \: we \: know \: that \: a^m \times a^n = a^{m+n}}$

$\bf \implies 3^{7 + r} = 3^4$

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Now, on both sides bases are same,

Therefore, powers will be equal

$\bf \implies 7 + r = 4$

$\bf \implies r = 4 - 7$

$\bf \implies r = - 3$

$\large \boxed{\bf r = - 3}$

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Question 3 :

$\bf Find \: k,$

$\bf 5^k = \dfrac{1}{25}$

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Solution :

$\bf 5^k = \dfrac{1}{25}$

$\bf 5^k = \dfrac{1}{5^{2}}$

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$\pink{\bf Now, \: we \: know \: that \: \dfrac{1}{a^{m}} = a^{-m}}$

$\bf \implies 5^k = 5^{-2}$

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Now, on both sides bases are same,

Therefore, powers will be equal

$\bf \implies k = -2$

$\large \boxed{\bf k = - 2}$