Question

(FUVEST) se log de 8 = a, então log 5 vale:

Answer 1

$log_{10}(8) = a \\\\ { 1 \over log_8(10) }= a \\\\ { 1 \over log_8(2 \times 5) } = a \\\\\ { 1 \over log_8(2) + log_8(5) } = a \\\\ { 1 \over \frac{1}{3} + log_8(5) }= a \\\\ log_8(5) = { 1 \over a} - { 1 \over 3} \\\\ log_8(5) = { 3 - a \over 3a } \\\\ {log(5) \over log(8)} = { 3 - a \over 3a} \\\\ { log(5) \over a } = { 3 - a \over 3a} \\\\\ \boxed{ log(5) = {3 - a \over 3} = 1 - { a \over 3} }$