Question

find the value of m 5^m-3×3^2m-8=225​

Answer 1

Given: The term 5^(m-3) x 3^(2m-8) = 225​

To find: The value of m?

Solution:

• Now we have given the term:

               5^(m-3) x 3^(2m-8) = 225​

• We can rewrite it as:

               5^(m-3) x 3^(2m-8) = 15^2

• We can write 15 as 5 x 3, so:

               5^(m-3) x 3^(2m-8) = (5 x 3)^2

• Now splitting it, we get:

               5^(m-3) x 3^(2m-8) = 5^2 x 3^2

• As the bases are same, so equating the corresponding powers, we get:

               m-3 = 2 and 2m - 8 = 2

               m = 5 and 2m = 10

               m = 5 and m = 5

Answer:

          So the value of m is 5.