Let's solve the problem in the image.

The problem is:

Hitunglah nilai dari $4^{x+1} - 8^x$ jika diketahui bahwa $2^x = 3$

Solution

1. Express $4^{x+1}$ and $8^x$ in terms of $2^x$:

   • Since $4 = 2^2$, we can rewrite $4^{x+1}$ as: $4^{x+1} = (2^2)^{x+1} = 2^{2(x+1)} = 2^{2x + 2}$
   • Since $8 = 2^3$, we can rewrite $8^x$ as: $8^x = (2^3)^x = 2^{3x}$

2. Substitute $2^x = 3$ into the expressions:

   • First, calculate $2^{2x + 2}$: $2^{2x + 2} = 2^{2x} \cdot 2^2 = (2^x)^2 \cdot 4$ Since $2^x = 3$, substitute this into the expression: $(2^x)^2 = 3^2 = 9$ So: $2^{2x + 2} = 9 \cdot 4 = 36$
   • Next, calculate $2^{3x}$: $2^{3x} = (2^x)^3 = 3^3 = 27$

3. Substitute and solve:

   • Now we substitute these values into the expression $4^{x+1} - 8^x$: $4^{x+1} - 8^x = 36 - 27 = 9$

Answer:

The correct answer is 9, which corresponds to option B.

Would you like more details on any steps, or do you have additional questions?

Here are five related questions that explore similar concepts:

1. How would you approach solving $4^{x+2} - 16^x$ if $2^x = 5$?
2. What is the general method for converting expressions like $8^x$ and $16^{x+1}$ using $2^x$?
3. How do you simplify $4^{2x} - 2^{4x}$ if $2^x = k$?
4. If $3^x = 4$, how would you calculate $9^{x+1} - 27^x$?
5. What are the key steps for solving exponential expressions when given a value for $2^x$ or similar powers?

Tip: When handling powers, always look for ways to express terms with the same base for easy substitution.