( 4 x ) 4 x 4 = ( x 4 ) 4 4 x
Find the real value of x that satisfies the equation above.
If the answer is of the form a × 1 5 b , then submit the value of a + b .
Note: Here, x = 0 , 1 .
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Typo in fifth line. you have missed " ^ " before 1/4. May I suggest a few short cuts ?
1] After \ press THREE spaces and enter. So the next sentence would go to the next line.
2] when ever we have a single digit, {.} are not required. \frac {1}{2} can be written as
\frac12. But if there is a non-number keep space as follows. \sqrt2 is OK but \sqrtA is not. It should be \sqrt A or \sqrt{A}.
4 x 4 x 4 = ( x 4 ) 4 4 x = ( x 4 1 ) 4 x 4 = ( x 4 ) 4 x 4 1 x x 4 = x 1 6 x 4 1 Equating the powers : − x 4 = 1 6 x 4 1 x 4 1 5 = 2 4 x = 1 5 2 1 6 x = 2 1 5 2 a + b = 2 + 2 = 4
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( 4 x ) 4 x 4 ( x 4 1 ) 4 x 4 x x 4 Equating the powers : − x 4 Raising root of 4 : − x x 1 6 1 x x 1 − 1 6 1 x 1 6 1 5 Raising power of 16 : − x 1 5 Raising root of 15 : − x x x = ( x 4 ) 4 4 x = ( x 4 ) 4 x 4 1 = x 1 6 x 4 1 = 1 6 x 4 1 = 2 x 1 6 1 = 2 = 2 = 2 = 2 1 6 = 1 5 2 1 6 = 1 5 2 1 5 × 2 = 2 1 5 2
∴ a + b = 2 + 2 = 4