Question

logarithms question.​

Answer 1

Answer:

log(x)a.

Step-by-step explanation:

We know the base changing formula, using the same this can be done.

For the proof of base changing formula :

Let d = ec

⇒ b^d = b^( ec )

⇒ b^( ec ) = x             { let b^d = x }

⇒ ( b^e )^c = x

⇒ a^c = x                    { let b^e = a }

⇒ log(a) x = c

            Above, b^e = a

                    log(b) a = e

       Also,

            b^d = x

            log(b) x = d

At the starting we said, d = ec,

                  ⇒ log(b) x = log(b) a . log(a) x

                  ⇒ { log(b) x } / { log(b) a } = log(a) x

Hence we have now proved the base changing formula, now,

⇒ log(y)a x log(x)y

Changing the base of log(y)a:

⇒ { log(x)a / log(x)y } × log(x)y

⇒ log(x)a