Question

Write as an equivalent expression using the properties of logs:
logb(³√5x/12y^4)

*the b is little

Answer 1

\[\log_b(\sqrt[3]{\frac{5x}{12y^4}})\] can be rewritten as \[\log_b((\frac{5x}{12y^4})^{1/3})\]
In a logarithmic function, you can move the exponent to the coefficient.
\[\frac{1}{3}\log_b(\frac{5x}{12y^4})\]
Division in a logarthimic function is seen as subtraction outside. (I'll provide an example)
\[log_b\frac{y^3}{x^2}=log_b(y^3)-log_b(x^2)\]
Once you do that, you can once again move the exponent to the coefficient. (continuing with that example, here's the finished product)
\[log_b(y^3)-log_b(x^2)=3log_b(y)-2log_b(x)\]