The point (6,1)

lies on the graph of the function h(x)=log6x
. What point (not an intercept) is guaranteed to be on the graph of the function k(x)=6x
?

1 answer

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:

\[ \boxed{(1, 6)} \]