I need another person who knows there Math?

Question

Given log(base of c) x=1.2 and log(base of c)y=3.9, find using the property of logarithms:

a)log(base of c)times the square root of x=?

b.) log(base of c)(xy)=?

thank ou so much

Answer 1

Remember that with logarithms, exponents within the log become the coefficient outside the log.

1.) logc (sqrt x)
= logc (x^1/2)
= (1/2) logc x
= (1/2) * 1.2
= 0.6

If numbers are being multiplied within the log, they can be split up to the sum of the log of the numbers. It's a similar rule to that in problem 1, as you can imagine:

log (x^2) = log (x * x) = log x + log x = 2 log x

2.) logc xy
= logc x +logc y
= 1.2 + 3.9
= 5.1

Answer 2

a)
LOGc(sqrt X)
= LOGc(X)^1/2
= 1/2 LOGc(X)
= 0.6
** Note that if the log expression is denoted as LOGa(X)^b, it can only be rewrote as b*LOGa(X) if the power of b applies to the entire term X. i.e. you cant do this when you have say LOGc[XY^2]. Cos the power of 2 in Y does not apply for X.

b) LOGcXY = LOGcX + LOGcY = 1.2 + 3.9 = 5.1
** Another property of logarithm. When 2 log expressions OF THE SAME BASE are added together, the result can be written as LOGcXY (for the above case). The same is true for the converse. LOGcXY = LOGcX + LOGcY.

Hope this helps=)

Answer 3

logcx to the second power

Answer 4

a. 0.6


b. 5.1