Question

Write as a logarithm? 4(1/2)^x=8

Answer 1

\[4(\frac{ 1 }{ 2 })^{x}=8\]

Answer 2

$$
\log_2{4(\frac{ 1 }{ 2 })^{x}}=\log _24+x\log_2{\cfrac{1}{2}}=2-x\log_2 2=1-x=\log_2 8=3\\
$$
So,
$$
1-x=3\\
x=-2
$$

Answer 3

Make sense?

Answer 4

Correction:
$$
\log_2{4(\frac{ 1 }{ 2 })^{x}}=\log _24+x\log_2{\cfrac{1}{2}}=2-x\log_2 2=2-x=\log_2 8=3\\
2-x=3\\
x=2-3=-1
$$

Answer 5

\(\large{ \bf log_{\color{red}{ a}}{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}\\ \quad \\ \quad \\

4\left(\frac{ 1 }{ 2 }\right)^{x}=8\implies \left(\frac{ 1 }{ 2 }\right)^{x}=\cfrac{8}{4}\implies {\color{red}{ \left(\frac{ 1 }{ 2 }\right)}}^{x}={\color{blue}{ 2}}}\)

Answer 6

Yes, thank you!