Question

Answer in detail........​

Answer 1

Answer:

Step-by-step explanation:

7^(5x-8)×5^(x+2) = 30625

7^(5x-8)×5^(x+2) = 7^2×5^4

since x is an integer, therefore equate the power of equal bases from LHS and RHS

5x-8 = 2

5x = 10

x = 2

x+2 = 4

x = 2

a^x = b^y = c^z = t(let)

therefore,

a=t^(1/x) , b=t^(1/y) , c=t^(1/z)

a³ = b²c

t^(3/x) = t^(2/y) × t^(1/z)

t^(3/x) = t^(2/y + 1/z)

bases are same on both sides, therefore equating powers, we get

3/x = 2/y + 1/z

3/x - 2/y = 1/z