Answer:
5ln(u) + 30ln(v)
Step-by-step explanation:
To work this out, we'll use the following logarithmic laws of multiplication and exponents:
[tex]\log_a(m^n) = n\times\log_a(m)\\\log_a(m\times n)=\log_a(m)+\log_a(n)[/tex]
Working it out:
[tex]\ln\left(\left(uv^6\right)^5\right)\\\to 5\ln\left(uv^6\right)\\\to5\left(\ln(u)+\ln\left(v^6\right)\right)\\\to 5\left(\ln(u)+6\ln(v)\right)\\\\\to 5\ln(u)+30\ln(v)[/tex]
The logarithm ln(uv^6)^5 can be simplified to 5ln(u) + 30ln(v)
