Help with a log equation?

Question

Log 4 a = k

Solve log k 4

This is a maths equation I need to work out for homework and tryed and failed hopefully somebody will post a solution the answer is 1/k by the way but I need the solution?

Thanks

I mean
the log of a to the base 4 is k
E.G. log 4 a
4 is the base
E.G. log k 4
k is the base

i.e.
Log(4)*a=k

but the correct is answer is 1/k so does that mean log(k)a = 1

Answer 1

log[4]a = k, where [4] is the base.

Therefore, a = 4^k

Now take the log of both sides to the base [a].

log[a]a = k * log[a]4

1 = k * log[a]4

log[a]4 = 1 / k

This is not quite the same as you have, so have you asked to solve the correct expression?

If, from a = 4^k, you take the log to base [k], it becomes :

log[k]a = k * log[k]4

So, log[k]4 = log[k]a / k, instead of your answer 1/ k.

Answer 2

the log base 4 of a is equal to k.

=> 4^k = a

take the log base k of both sides

log(k) 4^k = log(k) a

by log rules:

klog(k) 4 = log(k) a

log(k) 4 = [log(k) a]/k

and there's your answer

Answer 3

log_4 a = k
a=4^k
log_k a = k* log_k 4

So, the answer is:
log_k 4 = (log_k a) / k


Where log_4 means "log to the base 4" etc.

Answer 4

your answer is wrong .. your real answer should be log
a base k ) / k

book is wrong