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Simplify the expression in the numerator on the left side.

Mathematics

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a) Find the value of xx if 4x32(x+1)+5x5=162x−15+x4^x \frac{32(x+1)+5x}{5} = \frac{16^{2x-1}}{5} + x.

Step 1: Simplify the expression in the numerator on the left side.

32(x+1)+5x=32x+32+5x=37x+3232(x+1) + 5x = 32x + 32 + 5x = 37x + 32

The equation becomes:

4x37x+325=162x−15+x4^x \frac{37x+32}{5} = \frac{16^{2x-1}}{5} + x

Step 2: Multiply the entire equation by 5 to eliminate the denominators.

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