Question

1. find the value of log 8base 2​

Answer 1

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

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.

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

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

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

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

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

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

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

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

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

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

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