Answer: The value of
is 5
Step-by-step explanation:
-Solve:
×
![=3^n](https://tex.z-dn.net/?f=%3D3%5En)
-If two numbers with exponents are multiplying together, then the exponents would add up together:
![3^5 = 3^n](https://tex.z-dn.net/?f=3%5E5%20%3D%203%5En)
-Simplify by the exponent:
![243 = 3^n](https://tex.z-dn.net/?f=243%20%3D%203%5En)
-Take the logarithm both sides of the equation:
![log(3^n)= log (243)](https://tex.z-dn.net/?f=log%283%5En%29%3D%20log%20%28243%29)
- Then, you divide both sides by
:
![n=\frac{log(243)}{log(3)}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7Blog%28243%29%7D%7Blog%283%29%7D)
- Use the change-of-base formula, which is
:
![n = log_{3}(243)](https://tex.z-dn.net/?f=n%20%3D%20log_%7B3%7D%28243%29)
![n = 5](https://tex.z-dn.net/?f=n%20%3D%205)
So, the value of
is 5.