Question

Find x if 2^x-7×5^x-4=1250

Answer 1

Hey mate,

2^(x - 7).5^(x - 4) = 1250

Prime factor of 1250,

1250 = 2 × 5 × 5 × 5 × 5

= 2¹ × 5⁴

so, 2^(x - 7).5^(x -4) = 2¹.5⁴

this is possible only when ,

2^(x -7) = 2¹ or 5^(x -4) = 4

(x - 7) = 1 or x - 4 = 4 , => x = 8

x = 8 ANSWER...

HOPE IT HELPS:-))

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.