Question

★ 50 points ★ question.

Pls, solve question 9, 11, 12, and 13 .
Answers are given .

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Answer 1

Answers with step-by-step explanation:

Question 9.

$\mathsf{\implies\dfrac{2^n + 2^{n+1}}{2^{n+1}-2^n}}\\\\\\\mathsf{\implies \dfrac{2^n + ( 2^n \times 2^1)}{(2^n \times 2^1)-2^n}}\\\\\\\mathsf{\implies \dfrac{2^n( 1 +2)}{2^n( 2 - 1 )}}\\\\\\\mathsf{\implies \dfrac{2+1}{1 }}\\\\\\\implies 3$

Question 10.

$\mathsf{\implies 2^{65} \times 2^{55} - 2^{93}\times2^{27}}\\\\\mathsf{\implies 2^{65+55}-2^{93+27}}\\\\\mathsf{\implies2^{120} - 2^{120}}\\\\\mathsf{\implies 0}$

Question 11.

$\mathsf{\implies 2^{n-7}\times5^{n-4}=1250}\\\\\mathsf{\implies 2^{n-7}\times5^{n-4}=2 \times625}\\\\\mathsf{\implies 2^{n-7}\times 5^{n-4}=2^1 x 5^4 }\\\\\mathsf{Comparing\:values\:,}\\\\\mathsf{2^{n-7}=2^1\quad Or \quad 5^{n-4}=5^4}\\\\\mathsf{n-7 =1\quad Or \quad n - 4 = 4}\\\\\mathsf{n=8}$

Question 12.

$\mathsf{\implies 25^{n-1} +100=5^{2n-1}}\\\\\mathsf{\implies 5^{2(n-1)}-5^{2n-1}=-100}\\\\\mathsf{\implies 5^{2n-2}-5^{2n-1}=-100}\\\\\mathsf{\implies \dfrac{5^2n}{5^2}-\dfrac{5^{2n}}{2}}=-100\\\\\\\implies \mathsf{5^{2n}}\bigg( \dfrac{1}{25}-\dfrac{1}{5}\bigg)=-100\\\\\\\implies \mathsf{5^{2n}\bigg( - \dfrac{4}{25}}\bigg) =-100\\\\\\\mathsf{\implies 5^{2n}=-100 \times \bigg( - \dfrac{25}{4}\bigg)}\\\\\\\implies \mathsf{5^{2n}=5^4}$

Comparing both sides,

2n = 4 ⇒ n = 4 / 2 ⇒ n = 2

Question 13.

$\mathsf{ \implies \dfrac{(3^n)^2 \times 3^2 \times 3^n-(3^3)^n}{(3^5)^3 x 8 }=\dfrac{1}{27}}\\\\\\\implies \mathsf{\dfrac{3^{2n}\times 3^2 \times 3^n-3^{3n}}{3^{15}\times 8}}=\dfrac{1}{27}\\\\\\\implies \mathsf{\dfrac{3^{2n+2+n}-3^{3n}}{3^{15}\times 8}=\dfrac{1}{27}}\\\\\\\implies \mathsf{\dfrac{3^{3n+2}-3^{3n}}{3^{15}\times8}=\dfrac{1}{27}}\\\\\\\mathsf{\implies \dfrac{3^{3n}(3^2 - 1 )}{3^{15}\times 8}}=\dfrac{1}{3^3}\\\\\\\mathsf{\implies \dfrac{3^{3n} \times 8}{3^{15}\times 8}}=\dfrac{1}{3^3}$

$\mathsf{\implies 3^{3n} =\dfrac{3^{15}}{3^3}}\\\\\\\implies \mathsf{3^{3n} =3^{15-3}}\\\\\implies \mathsf{3^{3n} =3^{12}}$

3n = 12

n = 12 / 3

n = 4

Answer 2

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Refer to the attachment .

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