For what values of b will F(x) = logo x be a decreasing function? A. b>0
B. 0 C. b< 0
D. O >b>-1

is a decreasing function when

This is because we can use the change of base formula to say

If b is between 0 and 1, not including either endpoint, notice how the log(b) term is negative.

For example, if b = 0.5, then log(b) = log(0.5) = -0.301 approximately. I'm using log base 10 to get log(0.5) = -0.301

So for b = 0.5, we have,

The log(x) part on its own is always increasing. The negative coefficient out front flips it to always decreasing.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)