Let $x$ be a real number such that $4^x = 4$. Find the value of $2^{5x+3}$. Express your answer as a number.See answer

Daftar Isi

Let x be a real number such that 4x 4 Find the value of 25x 3 Express your answer as a number

Question

Let $x$ be a real number such that $4^x = 4$. Find the value of $2^{5x+3}$. Express your answer as a number.

Basic Answer

Step 1: Solve for $x$

Given the equation $4^x=4$, we recognize that $4$ can be written as $4^1$. Therefore, we have:
$$4^x=4^1$$
This implies:
$$x=1$$

Step 2: Substitute $x$ into the expression $2^{5x+3}$

Now, we need to find the value of $2^{5x+3}$ when $x=1$. Substitute $x=1$ into the expression:
$$2^{5(1)+3}=2^{5+3}=2^8$$

Step 3: Calculate $2^8$

Calculate the value of $2^8$:
$$2^8=256$$

Final Answer

$$256$$