Question

Define Loga 5=3 then ?​

Answer 1

$\textsf{\large{\underline{Correct Question}:}}$

• If logₐ(5) = 3 then find the value of a.

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

Given That:

$\rm: \longmapsto log_{a}(5) = 3$

By definition of logarithm:

$\rm: \longmapsto { \alpha }^{ \beta } = \gamma \: \: or \: \: log_{ \alpha }( \gamma) = \beta$

Therefore:

$\rm: \longmapsto {a}^{3} = 5$

$\rm: \longmapsto a = \sqrt[ \rm3]{ \rm5}$

★ Which is our required answer.

$\textsf{\large{\underline{More To Know}:}}$

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

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

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

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

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

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

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

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

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

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