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Alex Ar [27]
3 years ago
7

Which of the following is the inverse of y=12^x

Mathematics
2 answers:
damaskus [11]3 years ago
8 0
y = 12^x


x = 12^y

12^y = x

\log 12^y = \log x

y \log 12 = \log x

y = \dfrac{\log x}{\log 12}



Elenna [48]3 years ago
3 0
y=12^x\ \ \ |log_{12}\\\\\log_{12}y=\log_{12}12^x\\\\\log_{12}y=x\log_{12}12\\\\x=\log_{12}y


y=12^x\to y^{-1}=\log_{12}x;\ x\in\mathbb{R^+}\to\ y^{-1}=\dfrac{\log x}{\log12};\ x\in\mathbb{R^+}\to y^{-1}=\dfrac{\ln x}{\ln 12}

Used:\\\\\log_aa=1\\\\\log_ab^n=n\log_ab\\\\\log_ab=\dfrac{\log_cb}{\log_ca}
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Read 2 more answers
Below are three different hypothesis tests about population proportions. For each test, use StatKey and the information given to
Ilia_Sergeevich [38]

Answer:

1a) p-hat=0.38

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1c) The null hypothesis is not rejected

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Step-by-step explanation:

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1a) The p-hat is p-hat=38/100=0.38.

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As it is a two-sided test, the p-value considers both tails of the distribution.

The p-value for this |z|=1.74 is P=0.08.

1c) The null hypothesis is not rejected.

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2a) The p-hat is p-hat=320/500=0.64.

2b) The standard deviation is

\sigma=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.7*0.3}{500}}=0.02

The sample size is n=500.

The z-value is:

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2c) The null hypothesis is rejected.

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As it is a two-sided test, the p-value considers both tails of the distribution.

The p-value for this |z|=1.43 is P=0.153.

2c) The null hypothesis is not rejected.

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