4.141304347826087
That's what I got when I did that
Answer:
a = -3
General Formulas and Concepts:
<u>Algebra I</u>
- Solving Exponential Equations
- Exponential Property [Rewrite]:
![\displaystyle b^{-m} = \frac{1}{b^m}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20b%5E%7B-m%7D%20%3D%20%5Cfrac%7B1%7D%7Bb%5Em%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em />
<em />
<em />
<u>Step 2: Solve for </u><em><u>a</u></em>
- Rewrite:
![\displaystyle 5^a = \frac{1}{5^3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Ea%20%3D%20%5Cfrac%7B1%7D%7B5%5E3%7D)
- Rewrite [Exponential Property - Rewrite]:
![\displaystyle 5^a = 5^{-3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Ea%20%3D%205%5E%7B-3%7D)
- Set:
![\displaystyle a = -3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%20%3D%20-3)
Check the picture below.
notice the reflected gray line on the red one over the y=x line, the slope of either line across the y=x line is simply the other's upside-down.
![\stackrel{\textit{slope of line "a"}}{a\implies \cfrac{a}{1}}\hspace{5em}\stackrel{\textit{slope of its reflection}}{\cfrac{1}{a}}](https://tex.z-dn.net/?f=%5Cstackrel%7B%5Ctextit%7Bslope%20of%20line%20%22a%22%7D%7D%7Ba%5Cimplies%20%5Ccfrac%7Ba%7D%7B1%7D%7D%5Chspace%7B5em%7D%5Cstackrel%7B%5Ctextit%7Bslope%20of%20its%20reflection%7D%7D%7B%5Ccfrac%7B1%7D%7Ba%7D%7D)