TOP QUESTIONS AND ANSWERS FOR YOU

Maths

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9th

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January 24, 2022

**2. Given log2 x = m and log5 y = n**

**(i) Express 2m-3 in terms of x**

Joslin Smith

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Student

Given, log2 x = m and log5 y = n

So,

2m = x and 5n = y

(i) Taking, 2m = x

2m/23 = x/23

2m-3 = x/8

Maths

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9th

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January 24, 2022

1. ** If loga m = n, express an – 1 in terms in terms of a and m.**

Joslin Smith

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Student

Maths

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9th

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January 24, 2022

**5. Find x, if:**

**(i) log3 x = 0**

Joslin Smith

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Student

We have, log3 x = 0

So, 30 = x

1 = x

Hence, x = 1

Maths

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9th

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January 24, 2022

Joslin Smith

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Student

Maths

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8th

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January 24, 2022

2. ** Express the following in exponential form:**

**(i) log8 0.125 = -1**

Joslin Smith

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Student

We know that,

loga c = b ? ab = c

(i) log8 0.125 = -1

8-1 = 0.125

Maths

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9th

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January 24, 2022

**1. Express the following in logarithmic form:**

**10-3 = 0.001**

Joslin Smith

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Student

Maths

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9th

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January 24, 2022

**Solve, using cross-multiplication:**** **

**8x + 5y = 9**

**3x + 2y = 4**

Joslin Smith

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Student

Maths

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9th

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January 24, 2022

**Solve, using cross-multiplication:**

**√2x – √3y = 0**

**√5x + √2y = 0**

Joslin Smith

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Student

Maths

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9th

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January 24, 2022

**2. The value of expression mx – ny is 3 when x = 5 and y = 6. And its value is 8 when x = 6 and y = 5. Find the values of m and n.**

Joslin Smith

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Student

Given,

The value of expression mx – ny is 3 when x = 5 and y = 6.

? 5m – 6n = 3 … (i)

And,

The value of expression mx – ny is 8 when x = 6 and y = 5

? 6m – 5n = 8 … (ii)

Solving for m and n:

Performing (i)×6 – (ii)×5, we get

30m – 36n = 18

30m – 25n = 40

(-) (+) (-)

____________

-11n = -22

So,

n = 22/11

n = 2

Now, on substituting n = 2 in equation (i), we get

5m – 6(2) = 3

5m = 15

m = 3

? The solution is m = 3 and n = 2.

Maths

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9th

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January 24, 2022

**Find the value of m, if x = 2, y = 1 is a solution of the equation 2x + 3y = m.**

Joslin Smith

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Student

Given, x = 2 and y = 1 is the solution of the equation 2x + 3y = m

Then,

2(2) + 3(1) = m

4 + 3 = m

? m = 7

Hence, if x = 2 and y = 1 is the solution of the equation 2x + 3y = m, then the value of m = 7.