Question

Find the value of x if 2^x-7 x 5^x-4=1250

Answer 1

2^( x - 7 ) × 5^( x - 4 ) = 1250

1250 = 2 × 5 × 5 × 5 × 5

2^( x - 7 ) × 5^( x - 4 ) = 2^1 × 5^4

So, x - 7 = 1

x = 7 + 1

x = 8

Answer 2

Correct question:

$\longrightarrow\rm{2^{(x - 7)} \times 5^{(x - 4)} = 1250}$

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Required answer:

$\longrightarrow\rm{2^{(x - 7)} \times 5^{(x - 4)} = 1250}$

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$\longrightarrow\rm{1250 = 2 * 5 * 5 * 5 * 5}$

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$\longrightarrow\rm{2^{(x - 7)} \times 5^{(x - 4)} = 2^{1} \times 5^{4}}$

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$\longrightarrow\rm{x - 7 = 1}$

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Transposing 7 to the other the other side, we get:

$\longrightarrow\rm{x = 7 + 1}$

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${\longrightarrow{\boxed{\rm{x = 8}}}}$

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Therefore, 8 is the required value of x in the given expression.