find the value of x if 2^x-7.5^x-4=1250
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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
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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