28 May Basic Maths

MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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What is log 100? • When nothing is written at base, we assume that it is log10 • We know that 10^2 = 100 • Therefore log 100 = 2 Ans.

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What is log 2 32? • We know that 2^5 = 32 • Therefore, log 2 32= 5 Ans.

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What is log 9 27? • We know that 3*3*3 = 27 • 3 comes when we square root 9. • Therefore first square root 9 and them make a power of 3. • Therefore the answer is ½*3= 3/2 Ans.

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What is log

25

25?

• We know that 25^1 = 25 • Therefore log 25 25 = 1

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Log 3 (1/243)? • 3*3*3*3*3 = 243 • But we know that when we have power in negative, we make it as denominator. • Therefore the answer is -5 Ans.

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Log

100

.1?

• .1 = 1/10 • We know that 10 comes in 100’s power as ½ • Therefore the answer is – ½ Ans.

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36

log64?

• We know that 36 = 6*6 = 6^2 • We can write it as: 6^2log64 • We can also write it as: 6log642 • We can write it as : 6log616 • 6log6= 1 • Therefore the answer is 16 Ans. www.afterschoool.tk

Log2(log381)? • Log381 = 4 • Therefore answer is 2 ans.

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What is log35*log2527 • • • • • •

We can write it as: (Log 5/ log 3 )* (log 27 / log 25) = (log 5/log 3) *(log 3^3 / log 5^2) = (log 5/log 3) *(3log 3 / 2log 5) = (log 5/log 3) *3/2(log 3 / log 5) 3/2 Ans. www.afterschoool.tk

How many digits are there in 2^64? Let us write it as: Log 10 2 64 Log 10 2 64 = 64log 10 2 Log 10 2 = .30103 64*.30103 = 19.26592. In this 19 is characteristic and .265 is mantissa. Characteristic is always one less than in number than number of digits. • Therefore the number of digits is 20 Ans. • • • • • • •

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Log

10

4.5?

• Log

10

4.5 = Log

10

9/2

• Log

10

4.5 = Log

10

9 - Log

• Log

10

4.5 = 2Log

• Log

10

4.5 = 2* .4771 - .30103

• Log

10

4.5 = .9542 - .30103

• Log

10

4.5 = .6542 Ans.

10

10

2

3 - .30103

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What is the area of isosceles triangles, whose one side is 6 cm and two equal sides are 5 cm each?

• Isosceles triangle is that triangle, which has two equal sides. • (s(s-a)(s-b)(s-c))^1/2 • S= 5+5+6 /2 = 8 • (8(3)(3)(2))^1/2 = 12

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Find the cost of painting a traingle shape @ 3 /- per square meter, whose base is 3, and height is 4 meters. It is right angle triangle? • Right angle triangle is one where one angle is of 90 degree. • Area of right angle triangle: • ½ (base * height) • = ½ (3*4) • =6 • Cost is 3 per sq. meter - so multiply it: • 6*3 = 18 Ans.

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