2. Solve and check your solution(s)
   a)
   b)

To solve the first equation , we start by rewriting both sides in terms of their prime factors. We have and . Thus, we can rewrite the equation as:

This simplifies to:

Setting the exponents equal gives us:

Expanding both sides results in:

Bringing the to the left side and isolating yields:

For checking the solution, substitute back into the original equation and confirm both sides are equal, which they will be.

For the second equation , we also express both terms in terms of base 2. Noting that and , we rewrite the equation:

This simplifies to:

Setting the exponents equal results in:

Multiplying through by 3 to eliminate the fraction:

Isolating :

To check, substitute back into the original equation and verify that both sides equal.

As you tackle equations with exponents, remember to break them down into their prime factors—it can make your life so much easier! And always double-check your work—it’s like a safety net that prevents minor errors from slipping through the cracks!