Find the value of x which satisfies the equation: 16^x = 8^x-1

Here are the solutions to the indices problems:

2. Find the value of $x$ which satisfies the equation: $16^x = 8^{x-1}$

Step 1: Express both bases as powers of the same prime number.

$$16 = 2^4$$ $$8 = 2^3$$

Step 2: Substitute these into the equation.

$$(2^4)^x = (2^3)^{x-1}$$

Step 3: Apply the power rule $(a^m)^n = a^{mn}$.

$$2^{4x} = 2^{3(x-1)}$$ $$$$