We can use three rules to solve this logarithm:
Power rule: [tex]\text{ln}(x^p)=p~\text{ln}(x)[/tex]
Product rule: [tex]\text{ln}(xy)=\text{ln}(x)+\text{ln}(y)[/tex]
Quotient rule: [tex]\text{ln}\frac{x}{y} = \text{ln}(x)-\text{ln}(y)[/tex]
Simplify each part of the logarithm:
4 In x → ln(x^4)
6 In y → ln(y^6)
In z → ln(z)
We multiply ln(x^4) and ln(y^6) according to the product rule and we divide it by ln(z) according to the quotient rule.
Therefore, the logarithm as a single quantity is [tex]\text{ln}\frac{x^4y^6}{z}[/tex]
Best of Luck!
