Logarithms Quiz Set 011

Speaking factually, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p, hence the answer, because 1 × 2 × 3 = 1 + 2 + 3. Expressions of the form $\text"log"_m(n) = p$ are same as m^p = n. We can see that none of the other options makes it correct.

From the theory of logarithms, we know that $\text"log"_m(√m)$ = $1/2$ × $\text"log"_m(m)$ = $1/2$ × 1 = 1/2.

We know log($1/{10m}$) = log(1) - (log(10) + log(m)) = 0 - (1 + 2) = -3.

$\text"log"_5(1024)$ is same as $\text"log"_5(4^5)$ = 5 × $\text"log"_5(4)$ = $5/{\text"log"_4(5)}$, which is same as $5/10$ = 1/2.

log(mn) = log(m) + log(n) always.