Question

Help please re simplifying a log expression

5xlog base 3 (1/x) + log base 3 (x^2) - 2xlog base 3 (sqrt x^3)

Answer 1

Please :)

Answer 2

log x + log y= log (x*y)
log x - log y = log (x/y)
x log y = log y^x

Answer 3

So is it then 1/x * x^2 then divide by x^1/2

Answer 4

not quite right

Answer 5

there is 5x

Answer 6

5x log_3 (1/x)= log_3(1/x)^5x

Answer 7

log_3((1/x)^5x * x^2)

Answer 8

but doesn't that then give me a negative?

Answer 9

log_3 (x^2/x^5)= log_3 (1/x^3)=log_3 (1/x)^3= 3 log_x (1/x)

Answer 10

now you have
3log_3(1/x)- 2x log_3 (sqrt(x^3))

Answer 11

now just do the same thing for the last part

Answer 12

is that then 1/x^3 divided by x^3/2?

Answer 13

log_3 ((1/x^3)/(sqrt(x^3))^5x)

Answer 14

log_3 ((1/x^3)/((x^3/2)^5x)= log_3((1/x^3)/(x^15x/2)
log_3(1/(x^3*x^15x/2)
log_3(1/x^(15x/2+3)
...

Answer 15

Sorry I am an idiot, why raise x^3/2 to ^5?

Answer 16

Thank you for all of your help xoxo