Question

pls solve these questions​

Answer 1

Solution 1

$1125\: =\: 3^{m} \: \times 5^{n}$

1125 if we will use LCM methodology you can get

$5\times5\times5\times3\times3$

So it's should be

$5^{3} \times 3^{2}$

take powers

m = 2

n = 3

Solution 2

$9 \times 3^{x} \: = \: (27)^{2x-3}$

$3^2\times3^{x} \: = \: 3^{3(2x-3)}$

$3^{2+x} \: = \: 3^{3(2x-3)}$

Take powers

2+x = 3(2x-3)

2+x = 6x - 9

2+9 = 6x-x

11 = 5x

x = 11/5

Solution 3

Sum of two rational number is $\dfrac{9}{20}$

One of them is $\dfrac{2}{5}$

Let second be x

$x \: + \: \dfrac{2}{5} \: = \: \dfrac{9}{20}$

$x \: = \: \dfrac{9}{20} \: - \: \dfrac{2}{5}$

$x \: = \: \dfrac{9\times5 \: - \: 2\times20}{20\times5}$

$x \: = \: \dfrac{45\: - \: 40}{100}$

$x \: = \: \dfrac{5}{100}$

$x \: = \: \dfrac{1}{20}$

Solution 4

As per question sum of two rational numbers is $-\dfrac{2}{3}$

Other one is $-\dfrac{8}{5}$

Let second one be y

To get the value of y follow the above steps used in question 3

Equation should be

$y \: + (\: \dfrac{-8}{5})\: = \: \dfrac{-2}{3}$

Answer should be

$-\dfrac{34}{15}$

Answer 2

ANSWER:

1st solution:

→ 1125 = 3^m × 5ⁿ

Taking LCM of 1125

5 | 1125

5 | 225

5 | 45

3 | 9

3 | 3

3 | 1

LCM of 1125 = 5³ × 3²

5³ × 3² = 5ⁿ × 3^m

Comparing

we get

n = 3 , m = 2

Hence , m = 2 , n = 3

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2nd solution:

Given

$\small{9 \times {3}^{x} = {27}^{2x - 3} } \\ \to {3}^{2} \times {3}^{x} = {3}^{3(2x - 3)} \\ using \: \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} \\ \to {3}^{2 + x} = {3}^{6x - 9} \\ using \: \: {a}^{ m} = {a}^{n} \implies m = n \\ \to2 + x = 6x - 9 \\ \to2 + 9 = 5x \ \\ \to x = \dfrac{11}{5}$

Hence, x = 11/5

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3rd solution:

Given

• Sum of 2 rational numbers is 9/20
• One of them is 2/5
• Other = ?

Let the other no. be x

→ x + 2/5 = 9/20

→ x = 9/20 - 2/5

→ x = 9/20 - 2(4)/2(5)

→ x = 9 - 8/20

→ x = 1/20

Verification:

Substituting the value of x in ther given equation

★ 1/20 + 2/5 = 9/20

Taking LHS

→ 1/20 + 2(4)/2(5)

→ 1+8/20

→ 9/20

LHS = RHS

Hence verified!

Hence the other no. is 1/20

______________________________

4th solution:

Given

• Sum of 2 rational numbers is -⅔
• One of them is -8/5
• Other no. = ?

Let the other no. be y

→ -8/5 + y = -⅔

→ y = -⅔+8/5

→ y = -10 + 24/15

→ y = 14/15

Verification:

Substituting the value of y in the given equation

★ -8/5 + 14/15 = -2/3

Taking LHS

→ -8(3)/5(3) + 14/15

→ -24/15 + 14/15

→ -10/15 = -2/3

LHS = RHS

Hence verified!

Hence , the other no. is 14/15