Question

Simplify your answer, type an integer or a simplified fraction

Answer 1

Answer:
`a)\text{ log}_216\text{ = 4}`

Step-by-step explanation:
`\begin{gathered} Given:\text{ } \\ a)\text{ }log_216 \\ \\ We\text{ need to find the value of the logarithm function above} \end{gathered}`

To determine the value, we will apply the logarithm rule:

`\begin{gathered} log_ba\text{ = }\frac{log\text{ a}}{log\text{ b}} \\ \\ applying\text{ same rule to the given function:} \\ log_216\text{ = }\frac{log\text{ 16}}{log\text{ 2}} \end{gathered}`
`\begin{gathered} \frac{log\text{ 16}}{log\text{ 2}}\text{ = }\frac{log\text{ 2}^4}{log\text{ 2}} \\ \\ One\text{ of the logarithm property is given as:} \\ log\text{ a}^b\text{ = blog a} \\ log\text{ 2}^4\text{ = 4 log2} \end{gathered}`
`\begin{gathered} \frac{log\text{ 2}^4}{log\text{ 2}}\text{ = }(4log2)/(log2) \\ log\text{ 2 is common to both numerator and denominator, so it cancels out} \\ \frac{log(\text{2})^(4)}{log\text{2}}=\text{ 4} \\ \\ Hence,\text{ log}_216\text{ = 4} \end{gathered}`