Question

25power x=125 power y
Then tell x²:y³​

Answer 1

Answer:

GIVEN :

If 25^x=125^y25

x

=125

y

then find the value of the ratio x:y

TO FIND :

The ratio of x:y

SOLUTION :

Given that the expression is 25^x=125^y25

x

=125

y

Solving the given expression 25^x=125^y25

x

=125

y

as below

(5^2)^x=(5^3)^y(5

2

)

x

=(5

3

)

y

By using the property of exponents :

(a^m)^n=a^{mn}(a

m

)

n

=a

mn

5^{2x}=5^{3y}5

2x

=5

3y

Since the bases are same we can equate the powers we get,

2x=3y

\frac{x}{y}=\frac{3}{2}

y

x

=

2

3

∴ x:y=3:2

∴ The ratio of x and y is 3:2