log(ax)^c What are the effects of a and what are the effects of c?

Answer 1

log (ax)^c = c log ax.

Now, we know that ax should be positive,

so when c increases, then definitely the logarithm also increases, and vice versa.



And, we know that "a" and "x" should have the same sign,

so,

if they are both positive, and as "a" increases, then also the logarithm increases, and vice versa.

Also,

if they are both negative, and as "a" increases, then the logarithm decreases, and vice versa.


^_^

Answer 2

Is this log base a or log ax^c?

if log base a (x)^c, then it can be rewritten as
(c)⋅loga(x) (exponents become multipliers)


loga(x) means a^(loga(x) = x

example with base 10 - no base # implies base 10

log10(x) means 10^{log(x)} =x

if x= 5, log(5) = 0.69897
so 10^(0.69897) = 5

example with base 2
log₂(y) means 2^{log₂(y)} = y
if y= 8, then log₂(8) = 3
so 2^{3}=8

Answer 3

log(ax)^c = c log(ax)

And:

c [ log(a) + log(x) ]

In other words, the exponent c multiples your result log(ax) by c.
And a adds log(a) to the result of log(x).