Question

I need help with number part a and bThank you very much

Answer 1

PART A

For our beautiful sun, we'll have that:

`b=1.4\cdot10^3`

This way,

`\begin{gathered} M=-2.5\log ((1.4\cdot10^3)/(2.84\cdot10^(-8))) \\ \\ \Rightarrow M=-9.74 \end{gathered}`

PART B

We'll have the equation:

`-0.27=-2.5\log ((b)/(2.84\cdot10^(-8)))`

Solving for b,

`\begin{gathered} -0.27=-2.5\log ((b)/(2.84\cdot10^(-8)))\rightarrow0.27=2.5\log ((b)/(2.84\cdot10^(-8))) \\ \\ \rightarrow(0.27)/(2.5)=\log ((b)/(2.84\cdot10^(-8)))\rightarrow0.108=\log ((b)/(2.84\cdot10^(-8))) \end{gathered}`

Now we'll use the following property:

`c=\log _a(b)\Leftrightarrow b=a^c`

This way,

`\begin{gathered} 0.108=\log ((b)/(2.84\cdot10^(-8)))\rightarrow e^(0.108)=(b)/(2.84\cdot10^(-8)) \\ \\ \Rightarrow b=2.84\cdot10^(-8)e^(0.108) \\ \\ \Rightarrow b=3.16\cdot10^(-8) \end{gathered}`