Logarithms Quiz Set 012

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.

We have 3 = log125 = log$5^3$ = 3 log 5, which gives log5 = 1. So, 2 = 2 × log5 = log$5^2$ = log25. Hence, the answer is 2.

log_x$(2/7)$ = $1/2$, by definition, gives $x^{1/2}$ = $2/7$. So x = $(2/7)^2$ = ${4/49}$.

Let log₂(128) = P. By definition, we have 2^P = 128 = 2⁷, which gives 7 as the answer.

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