1. Stating the problem: Solve the equations involving indices (exponents). Since the user did not provide specific equations, we will explain the general methods for solving equations with indices. 2. If the equation is of the form $a^x = a^y$, where $a > 0$ and $a \neq 1$, then by the property of equality of exponents, $x = y$. 3. For equations like $a^{f(x)} = b^{g(x)}$ where $a$ and $b$ are positive and not equal to 1, convert both sides to the same base if possible or take logarithms on both sides to solve for $x$. 4. For example, to solve $2^x = 8$, write $8$ as $2^3$ so the equation becomes $2^x = 2^3$. Therefore, $x = 3$. 5. Another example: Solve $3^{2x+1} = 27$. Rewrite $27$ as $3^3$ which gives $3^{2x+1} = 3^3$. Hence, $2x+1 = 3$. 6. Solve for $x$: $2x = 3 - 1 = 2$, so $x = 1$. 7. If the bases cannot be made the same, apply logarithms: for $a^{f(x)} = c$, take logarithm base $a$ or natural logarithm: $$ f(x) = \log_a c \quad \text{or} \quad f(x) = \frac{\ln c}{\ln a} $$ 8. Then solve for $x$ accordingly. This covers general steps for solving equations with indices/exponents. Final answer depends on specific equations given.