Math, asked by kalakantisravanthi, 2 months ago

1. find the value of log 8base 2​

Answers

Answered by anindyaadhikari13
8

\textsf{\large{\underline{Solution}:}}

We have to evaluate the given logarithm.

 \rm = \log_{2}(8)

Can be written as:

 \rm = \log_{2}( {2}^{3} )

We know that:

 \rm \longrightarrow \log_{a}( {x}^{n} )  = n \log_{a}(x)

Therefore:

 \rm =3 \log_{2}(2)

Also:

 \rm \longrightarrow \log_{a}(a)  = 1 \:  \:  \:  \{a \ne1 \: or \: 0 \}

Therefore, we get:

 \rm =3 \times 1

 \rm =3

Therefore:

 \rm \longrightarrow \log_{2}(8)  = 3

Which is our required answer.

\textsf{\large{\underline{Learn More}:}}

 \rm 1. \:  \:  {a}^{n} = b \implies log_{a}(b)  = n

 \rm 2. \:  \: log_{a}(1)  = 0, \: a \neq0,1

 \rm 3. \:  \: log_{a}(a)  = 1, \: a \neq0,1

 \rm 4. \:  \: log_{a}(x)  = log_{a}(y) \implies x = y

 \rm 5. \:  \: log_{e}(x) =  ln(x)

 \rm6. \:  \:  log_{a}(x) + log_{a}(y) = log_{a}(xy)

 \rm7. \:  \:  log_{a}(x) - log_{a}(y) = log_{a} \bigg( \dfrac{x}{y} \bigg)

 \rm 8. \:  \: log_{a}( {x}^{n} ) =  n\log_{a}(x)

 \rm 9. \:  \:  log_{a}(m) =  \dfrac{ log_{b}(m) }{ log_{b}(a) },m > 0,b > 0,a \ne1,b \ne1

 \rm 10. \:  \: log_{a}(b) = \dfrac{1}{ log_{b}(a) }


anindyaadhikari13: Thanks for the brainliest ^_^
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