Answer:
4.17
Step-by-step explanation:
We have been given an expression \(\text{log}_2(18)\). 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:
\(2^x=18\)
Upon taking natural log of both sides we will get,
\(\text{ln}(2^x)=\text{ln}(18)\)
Using property \(\text{ln}(a^b)=b\cdot \text{ln}(a)\) we will get,
\(x\cdot \text{ln}(2)=\text{ln}(18)\)
\(\frac{x\cdot \text{ln}(2)}{\text{ln}(2)}=\frac{\text{ln}(18)}{\text{ln}(2)}\)
\(x=\frac{2.8903717578961647}{0.6931471805599453}\)
\(x=4.16992500144\approx 4.17\)
Therefore, the value of our given expression is 4.17.
