Question

☆☆☆☆ NEED HELP ☆☆☆☆

Answer the following question *with EXPLANATION*.

Answer 1

Hello,
The question belongs to the chapter real numbers.
Now,
If 2 is squared, cubed, multiplied 4 times and so on, the answer will be a multiple of 2.
Now,
If 5 is squared, cubed and so on the answer will end with 5.
For example:
5¹=5
5²=25
5³=125
5⁴=625
And so on....
Now, if 5 is multiplied with 2 or its multiple the answer will end with a zero.
For example:
2*5=10
4*5=20
4*125=500
8*125=1000
8*625=5000
And so on...
Now,
We know that any number as power of 2 gives a multiple of 2 and any power of 5 gives the answer ending with 5
We know that if a multiple of 2 is multiplied with a digit ending with 5 it will give answer ending with zero. (from above observations)

For example:
${2}^{x} \times {5}^{x}$
Let the value of x=1
So,2*5 = 10
If x= 2
2²*5² = 4*25 = 100
If x = 3
2³*5³ = 8*125 = 1000
If x =4
2⁴*5⁴=16*625 = 10000

And so on....
Hence, from above all the observations
We can conclude that there is no number for x such that the value of 2^x *5^x ends with 5.

Hope this will be helping you

WARM REGARDS
Sahil khirwal