2^x-7x 5^x-4= 1250

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Solution

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

first of all find 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

hence x = 8

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Find x if

2^x-7 × 5^x-4 = 1250

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