Answer
graph of $g(x)=\log_7x$
Work Step by Step
Substituting $x=1,7,49,343,$ the corresponding values of $g(x)$ in the given function, $g(x)=\log_7x,$ are as follows:
\begin{align*}\require{cancel}
\text{If }x=1:
g(1)&=\log_7 1
\\&=
0
&(\log_b1=0)
\\\\
\text{If }x=7:
g(7)&=\log_7 7
\\&=
1
&(\log_b b=1)
\\\\
\text{If }x=49:
g(49)&=\log_7 49
\\&=
\log_7 7^2
\\&=
2\log_7 7
&(\log_b m^n=n\log_b m)
\\&=
2(1)
&(\log_b b=1)
\\&=
2
\\\\
\text{If }x=343:
g(49)&=\log_7 343
\\&=
\log_7 7^3
\\&=
3\log_7 7
&(\log_b m^n=n\log_b m)
\\&=
3(1)
&(\log_b b=1)
\\&=
3
.\end{align*}
Plotting the points $(1,0), (7,1), (49,2), (343,3)$ gives the graph of $g(x)=\log_7x$.
