Question

pls give answer with proper explanation​​

Answer 1

Question : -

If the mean of 28,34,41,23,45,18,21 is 'x' , then the value of $\sf{ 2 - log_{x} 2 - log_{x} 3 - log_{x} 5 }$ is ....

ANSWER

Given : -

Mean of 28,34,41,23,45,18,21 is 'x'

Required to find : -

Value of $\sf{ 2 - log_{x} 2 - log_{x} 3 - log_{x} 5 }$

Solution : -

Given Observations are;

28,34,41,23,45,18,21

No. of observations = 7

Sum of the observation is

= 28 + 34 + 41 + 23 + 45 + 18 + 21

= 210

Now,

Mean = (sum of observations)/(no. of observations)

This implies;

Mean = (210)/(7)

Mean = 30

• => x = 30

Now,

Required value to be evaluated is !!

$\sf{ 2 - log_{x} 2 - log_{x} 3 - log_{x} 5 }$

This implies;

$\sf 2 - log_{x}(2) - log_{x}(3) - log_{x}(5) \\ \sf \: taking \: - \: common \\ \\ \sf 2 - \big \{ log_{x}(2) + log_{x}(3) + log_{x}(5) \big \} \\ \\ \sf 2 - \{ log_{x}(2 \times 3 \times 5) \} \\ \\ \sf 2 - \{ log_{30}(30) \} \\ \\ \sf 2 - 1 \\ \\ \sf \implies 1$

Note : -

• log a + log b = log (ab)
• $\sf{log_{a} a = 1 }$

Therefore,

$\underline{\boxed{\mapsto{\sf{\green{ 2 - log_{x} 2 - log_{x} 3 - log_{x} 5 = 1 }}}}}$

Answer 2

Given,

• The Mean Of 28,34,41,23,45,18,21 is X.

To Find,

$2 - log_{x}(2) - log_{x}(3) - log_{x}(5)$

Solution,

$: \implies The \: \: Mean = \frac{Sum \: \: of \: \: Total \: \: Observation}{Number \: \: of \: \: Total \: \: Observation} \\ \\ : \implies x = \frac{28 + 34 + 41 + 23 + 45 + 18 + 21}{7} \\ \\ : \implies x = \frac{210}{7} \\ \\ : \implies \color{red} \boxed{x = 30}$

$: \implies 2 - log_{x}(2) - log_{x}(3) - log_{x}(5) \\ \\ : \implies 2 - ( log_{30}(2) + log_{30}(3) + log_{x}(5) ) \\ \\ : \implies 2 - ( log_{30}(2 \times 3 \times 5) ) \\ \\ : \implies 2 - ( log_{30}(30) ) \\ \\ : \implies 2 - 1 \\ \\ : \implies 1$

Required Answer,

1