Question

What is the value of the logarithmic or exponential expression?

Answer 1

`\begin{gathered} a)\text{ True} \\ b)\text{ False} \\ c)\text{ False} \end{gathered}`

Step-by-step explanation:

Here, we want to get the value of the logarithmic or exponential expression

a)

`\begin{gathered} The\text{ general rule here is:} \\ a^{log\placeholder{⬚}_ab}\text{ = b} \\ \\ Thus: \\ 2^{4log\placeholder{⬚}_23}\text{ = 2}^{log\placeholder{⬚}_23^4}\text{ = 2}^{log\placeholder{⬚}_281}\text{ = 81} \end{gathered}`

Thus, the above statement is true

b)

`\begin{gathered} ln\text{ e}^{(3)/(2)} \\ =\text{ }(3)/(2)ln\text{ e} \\ ln\text{ e = 1} \\ =\text{ }(3)/(2)*1\text{ = }(3)/(2) \end{gathered}`

The above is false

c)

`\begin{gathered} 2ln\text{ e = 2} \\ we\text{ now have} \\ e^(3+2)\text{ = e}^5 \end{gathered}`

This means that the above statement is false