Question

find the value of log 1/343 to the base 7​

Answer 1

To find -

$log_{7}( \frac{1}{343} ) = - a$

Solution -

$log_{7}( \frac{1}{343} ) = - a$

$log_{7}(343 {}^{ - 1} ) = - a$

$log_{7}( {7}^{ - 3} ) = - a$

$- 3 log_{7}(7) = - a$

$- 3 \times 1 = - a$

$- 3 = - a$

$a = 3$

Additional information -

Laws of logarithm -

$1) log_{a}(a) = 1$

$2) log_{a}(1) = 0$

$3) log_{a}(mn) = log_{a}(m) + log_{a}(n)$

$4) log_{a}( \frac{m}{n} ) = log_{a}(m) - log_{a}(n)$

$5) log_{a}( {m}^{p} ) = p log_{a}(m)$

$6) log_{c}(b) = \frac{ log_{a}(b) }{ log_{a}(c) } (a \: and \: b \: are \: positive \: real \: numbers \: and \: a \: and \: b \: not \: equal \: to \: 1)$