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4 years ago

Express in exponential form. log3 27 = 3

Mathematics

2 answers:

kirill [66]4 years ago

5 0

Answer:

$3^3 = 27$

Step-by-step explanation:

$log_3(27)=3$

WE need to convert it into exponential form

Rule for converting log into exponential form is

$log_b(x)=a$ exponential form is $b^a = x$

base of log becomes the base of exponential form

$log_3(27)=3$ can be written as $3^3 = 27$

ollegr [7]4 years ago

4 0

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~~~~~~

How you right ANY log in Exponential form is like this:

Log_x Z = y

x^y = Z

So...

Log_3 27 = 3

3^3 = 27 would be your answer...

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4 years ago

Find the variance of the following data. Round your answer to one decimal place. x 1 2 3 4 5 P(X=x) 0.3 0.2 0.2 0.1 0.2

Reptile [31]

The variance of a distribution is the square of the standard deviation

The variance of the data is 2.2

<h3>How to calculate the variance</h3>

Start by calculating the expected value using:

$E(x) = \sum x* P(x)$

So, we have:

$E(x) = 1 * 0.3 + 2* 0.2 +3 * 0.2 + 4 * 0.1 + 5 * 0.2$

This gives

$E(x) = 2.7$

Next, calculate E(x^2) using:

$E(x^2) = \sum x^2* P(x)$

So, we have:

$E(x^2) = 1^2 * 0.3 + 2^2* 0.2 +3^2 * 0.2 + 4^2 * 0.1 + 5^2 * 0.2$

$E(x^2) = 9.5$

The variance is then calculated as:

$Var(x) = E(x^2) - (E(x))^2$

So, we have:

$Var(x) = 9.5 - 2.7^2$

$Var(x) = 2.21$

Approximate

$Var(x) = 2.2$

Hence, the variance of the data is 2.2