Question

\[\sqrt{16x ^{3}}/\sqrt{4x}\]

Answer 1

start by simplifying the constants. What do you notice about 4 and 16?

Answer 2

factor 4x

Answer 3

or just 4

Answer 4

A couple properties you should know first\[\sqrt x=x^{1/2}\]\[\sqrt ab=\sqrt a \sqrt b\]\[(x^a)^b=x^{ab}\]

Answer 5

start with the constants. You should see immediately that they are perfect squares

Answer 6

4 and 2

Answer 7

yes. so now you have \[4\sqrt x^3 \over 2\sqrt x\]

Answer 8

change the radical sign to 1/2 power to make things easier

Answer 9

\[4(x^{1/2})^3 \over 2x^{1/2}\]

Answer 10

now looking at the properties I posted finish the problem

Answer 11

\[{x^a \over x^b }= x^{a-b}\]

Answer 12

x^1/2(3)
for the top half right

Answer 13

keep going

Answer 14

4(x)^1/3

Answer 15

No i would multiply the bottom half now

Answer 16

\[\color{red}4(x^{1/2})^3 \over \color{red}2x^{1/2}\]\[\color{red}2(x^\color{blue}{{1/2}})\color{blue}{^3} \over x^{1/2}\]\[\color{red}2x^\color{blue}{{3/2}} \over x^{1/2}\]Now simplify the numerator and denominator using:\[{x^a \over x^b }= x^{a-b}\]

Answer 17

ok so it would be 2x(3/2-1/2= 2/2 which is one ) so just 2x

Answer 18

correct!! Good job! Do you understand all the steps?

Answer 19

yea i just need to remember the rules

Answer 20

log\[\log_{6} (x-5)+\log_{6} ^x=2\]

Answer 21

\[\log_a x + \log_a y=\log_a xy\]\[\log_a x - \log_a y = \log_a x/y\]

Answer 22

\[\log_a x = y \rightarrow a^y = x\]

Answer 23

you should be able to solve now. take your time, I'm just making dinner

Answer 24

BTW, once you get rid of the log, you should see a polynomial. You need to get it in the form: 0 = ax^2 + bx +c, so that you can factor or use the quadratic to solve for x

Answer 25

what do i do with the 2

Answer 26

see my 3rd equation

Answer 27

\[\log_{6} (x-5)+\log_{6} x=2\]\[\log_6 x(x-5)=2\]\[\log_6 x^2-5x=2\]\[x^2-5x=6^2\]\[x^2-5x-36=0\]You should be at this point. The log is gone and we have to solve for x. We can factor it or use the quadratic. Are you familiar with either of those methods?