Question

1 % log 8 2 + 1 %log 4 2​

Answer 1

SOLUTION:

We have to evaluate the given logarithm.

$\rm = \dfrac{1}{ \log_{8}(2) } + \dfrac{1}{ \log_{4}(2) }$

We know that:

$\rm \longrightarrow \log_{a}(b) = \dfrac{1}{ \log_{b}(a) }$

Using this formula, we will get:

$\rm = \log_{2}(8) + \log_{2}(4)$

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

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

$\rm = 3 \times 1 + 2 \times 1$

$\rm = 3 + 2$

$\rm = 5$

Therefore:

$\rm \longrightarrow \dfrac{1}{ \log_{8}(2) } + \dfrac{1}{ \log_{4}(2) } = 5$

LEARN MORE:

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

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

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

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

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

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

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

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

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

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