Question: Like can I do it like this
1. Let's analyze the expressions you wrote and see if they are correct.
2. You wrote: $$2^{6} + 12 = 0$$. This is not true because $$2^{6} = 64$$, and $$64 + 12 = 76 \neq 0$$.
3. Then you wrote: $$t + 12 = 0$$. This is a simple linear equation. To solve for $$t$$, subtract $$12$$ from both sides:
$$t + 12 = 0$$
$$t = 0 - 12$$
$$t = -12$$
4. Next, you wrote: $$2^{x/2} = 2$$. Since $$2 = 2^{1}$$, the exponents must be equal:
$$\frac{x}{2} = 1$$
Multiply both sides by 2:
$$x = 2$$
5. You also wrote: $$2^{x} = 4$$. Since $$4 = 2^{2}$$, then:
$$x = 2$$
6. Then: $$2^{x/2} = 6$$. This is not a power of 2, so to solve for $$x$$, take the logarithm base 2:
$$\frac{x}{2} = \log_{2}(6)$$
Multiply both sides by 2:
$$x = 2 \log_{2}(6)$$
7. Finally: $$2^{x} = 36$$. Take logarithm base 2:
$$x = \log_{2}(36)$$
Summary:
- For equations like $$2^{x} = a$$, solve by taking $$x = \log_{2}(a)$$.
- For linear equations like $$t + 12 = 0$$, isolate the variable by subtracting 12.
Your approach is mostly correct, but be careful with the values and the steps you take.