Answer:
4.17
Step-by-step explanation:
We have been given an expression [tex]\text{log}_2(18)[/tex]. We are asked to find the value of our given expression.
We can interpret our given expression as 2 raised to some power equals 18 and we need to find that power (x). We can represent our given information in an equation as:
[tex]2^x=18[/tex]
Upon taking natural log of both sides we will get,
[tex]\text{ln}(2^x)=\text{ln}(18)[/tex]
Using property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex] we will get,
[tex]x\cdot \text{ln}(2)=\text{ln}(18)[/tex]
[tex]\frac{x\cdot \text{ln}(2)}{\text{ln}(2)}=\frac{\text{ln}(18)}{\text{ln}(2)}[/tex]
[tex]x=\frac{2.8903717578961647}{0.6931471805599453}[/tex]
[tex]x=4.16992500144\approx 4.17[/tex]
Therefore, the value of our given expression is 4.17.
