To solve this problem you must apply the proccedure shown below:
1. You have the Change of base formula:
[tex] loga(x)=\frac{logb(x)}{logb(a)} [/tex]
2. Therefore, you have:
[tex] b=10\\log4(27)=\frac{log(27)}{log(4)} =2.377 [/tex]
3. To convert the original expression to a logarithm in base [tex] 2 [/tex], you apply the same property, but with [tex] b=2 [/tex]:
[tex] log4(27)=\frac{log2(27)}{log2(4)} [/tex]
4. Now, simplify the expression by applying the following property:
[tex] loga(a)=1\\ alog(b)=log(b^{a})
[/tex]
[tex] \frac{log2(3^{3})}{log2(2^{2})} =\frac{3log2(3)}{2}=log2(3^{\frac{3}{2}})=log2(5.196) [/tex]
The answers are: [tex] 1) 2.377\\ 2) log2(5.196) [/tex]
