Question

If `2^(n-7) \times 5^(n-4) = 1250`, what is the value of `n`?

Answer 1

`n=8`

Explanation:

With exponential equations, one approach is to make the bases on both sides the same.

`2^(n-7) xx 5^(n-4) = 1250`

`2^(n-7) xx 5^(n-4) = 2 xx 5^4`

Now we can compare the indices of like bases.

`n-7 = 1 " " rarr n =8`

`n-4 = 4" "rarr n = 8`

Do not be tempted to multiply the `2 and 5!`

The indices are different so you may not.