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`