Question

Find a so that the graph of f(x)=loga x contains the point (14,4)

Answer 1

Okay, here we have this:

Considering the provided information we obtain the following when we replace the point in the function:

`\begin{gathered} y=\log _ax \\ 4=\log _a14 \end{gathered}`

Now, let's solve for a:

`\begin{gathered} 4=(1)/(\log_(14)\left(a\right)) \\ 4\log _(14)\mleft(a\mright)=1 \\ \log _(14)\mleft(a\mright)=(1)/(4) \\ a=\sqrt[4]{14} \end{gathered}`

Finally we obtain that a is equal to ⁴√14. We can check it in the following graph resulting from the function: