Given that log _2 3=m and log _2 5=n,express log_2 30 in terms of m and n

Answer 1

We can use the properties of logarithms to express log_2 30 in terms of m and n.

First, we can write log_2 30 as log_2 (2 * 3 * 5), since 2 * 3 * 5 = 30.

Using the product rule of logarithms, we can split this up into two separate logarithms:

log_2 (2) + log_2 (3) + log_2 (5).

Now, we know that log_2 (2) = 1, since any number raised to the power of 1 is equal to itself.

Using the given information, we can express log_2 (3) as m and log_2 (5) as n.

Therefore, log_2 30 = 1 + m + n.

So, log_2 30 can be expressed in terms of m and n as 1 + m + n.