Answer:
The expression is [tex]y = 64 + x^{3}[/tex].
Step-by-step explanation:
Let be [tex]\log y = 3\cdot (\log 4 + \log x)[/tex], the "log" component is refered to logarithms with base 10. By definition of logarithm and its properties, we derive an expression of [tex]y[/tex] in terms of [tex]x[/tex]:
[tex]\log y = 3\cdot (\log 4 + \log x)[/tex]
[tex]10^{\log y} = 10^{3\cdot (\log 4 + \log x)}[/tex]
[tex]y = 10^{3\cdot \log 4}+10^{3\cdot \log x}[/tex]
[tex]y = 10^{\log 4^{3}}+10^{\log x^{3}}[/tex]
[tex]y = 64 + x^{3}[/tex]
The expression is [tex]y = 64 + x^{3}[/tex].
