Solve for \( x \): \( 2^{x+1} = 16^{x-1} \).

["Solve for ( x ): Understanding the Equation ( 2^{x+1} = 16^{x-1} )", "Finding the value of ( x ) in exponential equations can be simplified when both sides share a common base. The equation ( 2^{x+1} = 16^{x-1} ) is a perfect example of how to apply properties of exponents to solve for ( x ) efficiently.", "### Step 1: Express Both Sides with the Same Base\nThe number 16 is a power of 2:\n[\n16 = 2^4\n]\nUsing this, rewrite the right side of the equation:\n[\n16^{x-1} = (2^4)^{x-1} = 2^{4(x-1)}\n]\nNow substitute back into the original equation:\n[\n2^{x+1} = 2^{4(x-1)}\n]", "### Step 2: Compare Exponents\nSince the bases are identical, set the exponents equal to each other:\n[\nx + 1 = 4(x - 1)\n]", "### Step 3: Solve the Linear Equation\nExpand and simplify:\n[\nx + 1 = 4x - 4\n]\nBring all ( x )-terms to one side:\n[\n1 + 4 = 4x - x\n]\n[\n5 = 3x\n]\nSolve for ( x ):\n[\nx = \frac{5}{3}\n]", "### Conclusion\nThe solution to the equation ( 2^{x+1} = 16^{x-1} ) is ( x = \frac{5}{3} ). Mastering this method improves your ability to solve logarithmic and exponential equations efficiently.", "#### Want to Master More Algebra?\nExplore additional resources and practice problems on exponential equations and logarithms to build a strong foundation in algebra. Understanding how to match bases and equate exponents opens the door to solving complex equations with confidence.", "---", "Keywords: solve for ( x ), exponential equation, ( 2^{x+1} = 16^{x-1} ), algebra, logarithms, exponent rules, step-by-step solution, math tips, math help, equation solver"]