Use the properties of logarithms to write the expression as a single logarithm:

Question

7 ln x - 1/4 ln y

 

I would be very grateful for some help! Thanks for reading!

Answer 1

log_caⁿ = n*log_ca

                                a
log_ca - log_cb = log_c --- 
                                b

log_ca + log_cb = log_c(ab) 
~~~~~~~~~~~~~~~~~~~ 

7 ln x  - (1/4) ln y =

ln x⁷  -  ln y^1/4 =

       x⁷             x⁷  
ln ------ = ln ----
     y^{1/4           4}√y

Answer 2

7 ln(x)-(1/4)ln(y)

7 ln(x)=ln(x^7)

(1/4)ln(y)=ln[y^(1/4)]

ln(x^7)-ln[y^(1/4)]=ln[(x^7)/(y^(1/4))]