log3 (7x) logb(ac^3)

I suppose that you want to practice the properties of
logarithms on the following logarithms:

log3 (7x) and logb
(a*c^3)

To calculate the 1st logarithm, we'll have to apply
the product property:

log3 (x*y) = log x + log
y

Comparing, we'll get:

log3
(7x) = log3 (7) + log3 (x)

We'll apply the same property
for the 2nd logarithm:

logb (a*c^3) = logb (a) + logb
(c^3)

We need to apply the power property, to the second
term of the sum:

logb (c^3) = 3*logb
(c)

We notice that the superscript goes down in front of
the logarithm.

logb (a*c^3) = logb (a) + 3*logb
(c)

Therefore, applying the proper
properties, the requested logarithms
are:

log3 (7x) = log3 (7) +
log3 (x) and logb (a*c^3) = logb (a) + 3*logb (c)