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

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Answer 1 · 2018-07-09T07:48:54

#n=8#

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.