Logarithms Quiz Set 020

${\text"log"(√7)}/{\text"log"(7)}$ is same as ${\text"log"(7^{1/2})}/{\text"log"(7)}$, which is same as (1/2) × ${\text"log"(7)}/{\text"log"(7)}$ = 1/2.

Speaking factually, $\text"log"_m(n)$ = $1/{\text"log"_n(m)}$, hence the answer. Expressions of the form $\text"log"_m(n) = p$ are same as m^p = n. We can see that none of the options makes it correct. Also, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p.

log_x$(5/3)$ = $1/2$, by definition, gives $x^{1/2}$ = $5/3$. So x = $(5/3)^2$ = ${25/9}$, which is same as: $2{7/9}$.

log(m) + log(1/m) = log (m × $1/m$) = log 1 = 0.

log_x$(2/4)$ = $1/2$, by definition, gives $x^{1/2}$ = $2/4$. So x = $(2/4)^2$ = ${1/4}$.