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White raven [17]
2 years ago
6

Demonstrate two different ways to solve the equation 5^(2x+1) = 25.

Mathematics
1 answer:
Tanzania [10]2 years ago
3 0

Answer:

Step-by-step explanation:

Method 1: Taking the log of both sides...

So take the log of both sides...

5^(2x + 1) = 25

log 5^(2x + 1) = log 25 <-- use property: log (a^x) = x log a...

(2x + 1)log 5 = log 25 <-- distribute log 5 inside the brackets...

(2x)log 5 + log 5 = log 25 <-- subtract log 5 both sides of the equation...

(2x)log 5 + log 5 - log 5 = log 25 - log 5

(2x)log 5 = log (25/5) <-- use property: log a - log b = log (a/b)

(2x)log 5 = log 5 <-- divide both sides by log 5

(2x)log 5 / log 5 = log 5 / log 5 <--- this equals 1..

2x = 1

x=1/2

Method 2

5^(2x+1)=5^2

2x+1=2

2x=1

x=1/2

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A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

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The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the claim that they want to test is: "The true proportion of adults that would erase all their personal information online if they could is 0.39 or 39%". So we want to check if the population proportion is different from 0.39 or 0.39%, so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.

Part a. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.

p=0.39, where p the parameter of interest represent the true proportion of adults that would erase all their personal information online if they could

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