Simplify the expression in the numerator on the left side.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
a) Find the value of $x$ if $4^x \frac{32(x+1)+5x}{5} = \frac{16^{2x-1}}{5} + x$.
Step 1: Simplify the expression in the numerator on the left side.
$$32(x+1) + 5x = 32x + 32 + 5x = 37x + 32$$
The equation becomes:
$$4^x \frac{37x+32}{5} = \frac{16^{2x-1}}{5} + x$$
Step 2: Multiply the entire equation by 5 to eliminate the denominators.
$$5 \cdot 4^x
