Question

Please help w/ logarithms and if you do not know how to solve just let me know and I'll exist the session :)

Answer 1

From the first table, we have;

Given that;

$f(x)=b^x$

But, table II gives;

Given that;

$g(x)=\log _b(x)$

Where b is same positive constant for both equations.

Recall from a law of logarithm that;

$\text{If }\log _ba=c,\Leftrightarrow a=b^c$

Thus;

$\begin{gathered} g(x)=\log _b(x) \\ x=b^{g(x)} \\ \end{gathered}$$f(x)=7,x=1.404$

Also;

from the second table;

$x=10,g(x)=1.661$