Question

if log2, log 4, and log x are in ap, then find the value of x​

Answer 1

Answer:

The answer will be 8.

Step-by-step explanation:

Given A.P. is;

          log 2, log 4, log x

Thus, it can be concluded that;

a or first term = log 2;

d or difference = log 4 - log 2;

                          = log (4/2);              (since, log a - log b = log (a/b);)

                          = log 2;                          (i)

Again, d = log x - log 4;

Thus,   log 2 = log x - log 4;                      ( d = log 2, from eq.(i))

           log 2 = log (x/4);

Here, bases of log in LHS and RHS are same and we need to find the argument,

Thus,    2 = x/4;

            x = 4*2;

            x = 8;

That's all.