The function $g$ is given by $g(x)=lo{g}_{7}x,$ and the function $h$ is given by $h(x)=lo{g}_{49}x.$ Which of the following describes the relationships between $g$ and $h?$

For equal input values, the output values of $h$ are half the output values of $g.$

For equal input values, the output values of $h$ are twice the output values of $g.$

For equal input values, the output values of $h$ are the square of the output values of $g.$

For equal input values, the output values of $h$ are the square root of the output values of $g.$