Question

Exponents question…need help!!! 80 points up for grabs

Answer 1

Answer:

$2^{x+3}=24$

Step-by-step explanation:

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c$

$\begin{aligned}\implies 2^{x+3} & =2^x \cdot 2^3\\& = 2^x \cdot 8\end{aligned}$

$\textsf{Given }2^x=3:$

$\begin{aligned}\implies 2^{x+3} & = 2^x \cdot 8\\ & = 3 \cdot 8\\& = 24\end{aligned}$

Answer 2

Answer:

   24

Explanation:

Given 2^x = 3

Apply exponent rules

$\rightarrow \sf ln(2^x) = ln(3)$

$\rightarrow \sf x ln(2) = ln(3)$

$\sf \rightarrow x = \dfrac{ln(3)}{ln(2)}$

Then find the value of 2^{x + 3}

Insert x = ln(3)/ln(2)

$\rightarrow \sf 2^{\dfrac{\ln \left(3\right)}{\ln \left(2\right)} + 3}$

$\rightarrow \sf 24$