Question

please find it attached=- i need step by step explanation

Answer 1

Answer:

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Answer 2

Given:

• 5^y × 20^y = 10,000.

To Find:

• The value of y .

Answer:

Given that 5^y × 20^y = 10,000 ,

Now here we can observe that the base of two numbers are different but their powers or multiplicity are same .

And we know a formula that when we multiply two numbers with same powers but different bases as aⁿ × bⁿ = ( a × b ) ⁿ.

Using this , we have,

=> 5^y × 20^y = 10,000.

=> (5 × 20) ^y = 10,000.

=> (100)^y = 10,000.

=> (100)^y = (100 × 100).

=> (100)^y = (100)².

On comparing the bases and powers , we have,

→» y = 2 .

Hence the value of y is 2.