write the equation (1/4)^-7=16384 in logarithmic form?

Answer 1

First, 16384 = 4^7, therefore:

7 log_4 (4) = 7 = log_4 (16384), or:

7 log_4 (4) = log_4 (16384).

Here, log_4 means "logarithm to the base 4."

Of course, since log to ANY given base is simply a given multiple of log to any other fixed base, this equation is true for logs to ANY base, as well.

So, among other possible logarithmic equations, we could write:

7 log (4) = log (16384), and

7 ln (4) = ln (16384),

where unadorned 'log" is to base 10, and 'ln' is the 'natural logarithm, to base e.

You can also write the original equation as:

- 7 log (1/4) = log (16384)

or 7 log (1/4) = - log (16384),

again with the logarithms in any one of these being to the same base.

Technically, these aren't "different equations." They are merely different WAYS of writing the SAME equation, that is of writing the same equation in different FORMS.

I hope this has helped.

Live long and prosper.

Answer 2

(1/4)^-7=16384
-7 x log(1/4) = log(16384) (base 10)
7 x log(4) = log(16384) (base 10)
or
4^7 = 16384, So log(16384) = 7 (base 4)

Th

Answer 3

(1/4)^-7=16384
log(1/4)^-7= log16384
-7log(1/4)= log16384

Answer 4

take the log of both:
log((1/4)^-7)=log(16384)
then you can say:
-7*log(1/4)=log(16384)