The value of x is 1.66
Step-by-step explanation:
Let use revise the rules of exponential and logarithmic equations
1. If y =
, then ![log_{b}(y)=x](https://tex.z-dn.net/?f=log_%7Bb%7D%28y%29%3Dx)
2. ![log_{b}(y) = \frac{log(y)}{log(b)}](https://tex.z-dn.net/?f=log_%7Bb%7D%28y%29%20%3D%20%5Cfrac%7Blog%28y%29%7D%7Blog%28b%29%7D)
Use the rules above to solve the problem
∵ ![4^{x}+2=12](https://tex.z-dn.net/?f=4%5E%7Bx%7D%2B2%3D12)
- Subtract 2 from both sides
∴ ![4^{x}=10](https://tex.z-dn.net/?f=4%5E%7Bx%7D%3D10)
change the exponential equation to logarithmic equation
∴ ![log_{4}(10)=x](https://tex.z-dn.net/?f=log_%7B4%7D%2810%29%3Dx)
∵ ![log_{4}(10) = \frac{log(10)}{log(4)}](https://tex.z-dn.net/?f=log_%7B4%7D%2810%29%20%3D%20%5Cfrac%7Blog%2810%29%7D%7Blog%284%29%7D)
∴ x = ![\frac{log(10)}{log(4)}](https://tex.z-dn.net/?f=%5Cfrac%7Blog%2810%29%7D%7Blog%284%29%7D)
∴ x = 1.66
The value of x is 1.66
Learn more:
You can learn more about logarithmic function in brainly.com/question/10633485
#LearnwithBrainly
Answer:
Both -1.5 and -3/2 will be halfway between -2 and -1 on the number line. 3/2 will be halfway between 1 and 2. -4/3 will be between -1.5 and -1.
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