The point \((6, 1)\) lies on the graph of the function \(h(x) = \log_6 x\). This means that:
\[ h(6) = \log_6 6 = 1 \]
Since \(h(x) = \log_6 x\) and the logarithm is the inverse of the exponential function, we can find a related point on the graph of \(k(x) = 6^x\).
To find the corresponding \(x\) value for \(k(x)\), we take the \(y\) value from the point \((6, 1)\) which is \(x = 1\). We can then evaluate \(k(1)\):
\[ k(1) = 6^1 = 6 \]
Thus, the point \((1, 6)\) is guaranteed to be on the graph of the function \(k(x) = 6^x\).
So, the point that is guaranteed to be on the graph of the function \(k(x) = 6^x\) is:
\[ \boxed{(1, 6)} \]
1 answer