Question

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

Answer 1

24

Step-by-step 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 = (ln(3))/(ln(2))`

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

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

`\rightarrow \sf 2^{(\ln \left(3\right))/(\ln \left(2\right)) + 3}`

`\rightarrow \sf 24`

Answer 2

`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}`