Question

2^n-7 × 5^n-4 = 1250.
Then find the value of n.

Answer 1

${2}^{n - 7} \times {5}^{n - 4} = 1250 \\ \\ \\ \\ = > {2}^{n - 7} \times {5}^{n - 4} = 2 \times 625 \\ \\ \\ = > {2}^{n - 7} \times {5}^{n - 4} = {2}^{1} \times {5}^{4}$





On comparing values, we get


Taking, $2^{n - 7} = 2^{1}$


⏩ n - 7 = 1

⏩ n = 1 + 7

▶n = 8






$\boxed{ \bold{ \underline{Value \: \: o f \: \: n \: \: is \: \: 8}}}$

Answer 2

Heya!
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♦Given that =>
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$= > 2 {}^{n - 7} \times 5 {}^{n - 4} = 1250 \\ \\ = > 2 {}^{n - 7} \times 5 {}^{n - 4} = 2 \times 5 {}^{4}$


◾Comparing the Indices of the Like Bases ,


=> n - 7 = 1

=> n = 8..............(1)

.
=> n - 4 = 4

=> n = 8.............(2)



➡Hence the Value of n is 8


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