Logarithms Quiz Set 002

Expressions of the form $\text"log"_m(n) = p$ are same as m^p = n. We can see that if m = n, then p = 1 will make it correct. Also, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p.

${\text"log"(√6)}/{\text"log"(6)}$ is same as ${\text"log"(6^{1/2})}/{\text"log"(6)}$, which is same as (1/2) × ${\text"log"(6)}/{\text"log"(6)}$ = 1/2.

Let log₂(16) = P. By definition, we have 2^P = 16 = 2⁴, which gives 4 as the answer.

We have $\text"log"_3(4)$ + $\text"log"_3(4P + 1)$ = $\text"log"_3(3)$ + $\text"log"_3(P + 4)$. It is same as $\text"log"_3(4 × (4P + 1))$ = $\text"log"_3(3 × (P + 4))$. Equating the logs, $4 × (4P + 1) = 3 × (P + 4)$, solving for P we get P = ${8/13}$.

Expressions of the form $\text"log"_m(n) = p$ are same as m^p = n. We can see that if m = n, then p = 1 will make it correct. Also, log(m + n + p) = log(m × n × p) is possible only if m × n × p = m + n + p.