Math, asked by thundergodd1233, 7 months ago

If 100=2(power a) .5(power b) then find a+B.​

Answers

Answered by shanuraj4137
1

Answer:

If 100=2(power a) .5(power b) then find a+B.

Step-by-step explanation:

Given that 100!=2

a

3

b

5

c

7

d

...

We know that a,b,c,d are the exponents of 2,3,5,7 in 100!,

∴ Coefficient of 2 in 100! is

a=[

2

100

]+[

2

2

100

]+[

2

3

100

]+[

2

4

100

]+[

2

5

100

]+[

2

6

100

]+...

where [] represents the integral part of the number respectively,

∴ a=50+25+12+6+3+1+0+...=97

The exponent of 3 in 100! is

b=[

3

100

]+[

3

2

100

]+[

3

3

100

]+[

3

4

100

]+...

=33+11+3+1+0+...

=48

The exponent of 5 in 100! is,

c=[

5

100

]+[

5

2

100

]+...

=20+4+0+...

=24

The exponent of 7 in 100! is,

d=[

7

100

]+[

7

2

100

]+...

=14+2+0+...

=16

,

∴ c=

2

b

and d=

3

b

hope it's helpful

Answered by sujeetkumar4612
0

Answer:

300

Step-by-step explanation:

a=50,,

b=250

because 2 =100

1=50

5=250

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