Logarithms

Question

Rewrite as a single logarithm:

 

2log₅(A) - log₅(B)+(1/3)log₅(C)-5log₅(D)

 

thank you for all the help!

 

Answer 1

2log₅(A) - log₅(B) + (1/3)log₅(C) - 5log₅(D)

 

Log property: b*log(a) = log(a^b)

 

     log₅(A²) - log₅(B) + log₅(C^1/3) - log₅(D⁵)

 

Rearranging:

 

     log₅(A²) + log₅(C^1/3) - (log₅(B) + log₅(D⁵))

 

Log properties:  log(a) + log(b) = log(ab),  log(c) - log(d) = log(c/d)

 

               A²C^1/3

     log₅ ( ----------)

                  BD⁵