Question

2^(n-8) x 5^(n-5) = 125 find out value of n ​

Answer 1

Step-by-step explanation:

125 = 5×5×5

125= 5^3

On substituting this in the above equation, we get

2^(n-8) × 5^(n-5) = 5^3

Divide both side by 5^(n-5)

2^(n-8) = 5^3/(5^(n-5))

Using identity [a^m ÷ a^n = a^(m-n)]

2^(n-8) = 5^(3-(n-5))

2^(n-8) = 5^(8-n)

Divide both side by 5^(8-n)

2^(n-8)/(5^(8-n)) = 1

Using identity [a^-m = 1/(a^m)]

2^(n-8) × 5^(n-8) = 1

Using identity [a^m × b^m = (ab)^m]

(2×5)^(n-8) = 1

10^(n-8) = 1. .... [ 10^0 = 1]

10^(n-8) = 10^0

Now the base is same so we can equate the powers

n-8 = 0

n = 8

Here's your answer

Hope this will help U

Please mark me as brainliest

Give thanks for my efforts Please.☺