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3 years ago

Solve the following equations. 3 ⋅ 62^x = 648

Mathematics

1 answer:

gayaneshka [121]3 years ago

7 0

Answer:

$x=1.56861$

Step-by-step explanation:

$62^x=648$

By using logarithms it becomes easier to solve this question because of the properties they have

From the property of logarithms

$loga^x=xloga$

Take logarithms on both sides

$log62^x=log648$

$\Rightarrow xlog62=log648$

$\Rightarrow x=\frac{log648}{log62}$

$\Rightarrow x=1.56861$

$x=1.56861$

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Step-by-step explanation:

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SO, Null Hypothesis, $H_0$ : $\mu$ = 2,000 psi {means that the mean breaking strength of their climbing rope is 2,000 psi}

Alternate Hypothesis, $H_A$ : $\mu$ < 2,000 psi {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}

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So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.

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$\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645$

$\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645$

$(\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645$

$-0.27044 \times \sqrt{n}< -1.645$

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