What is the base of the function F(x) = b to the power of x if the graph has points of (1/3, 2)and another off the subject one if g(x)= log 7 x what is g(1/49)?

If F(x) = 2 when x = 1/3, and if the ntio is of the form
F(x) = b^x, then
2 = b^(1/3)
Cube both sides of the equation.
b = 8

If g(x) = log (7x), then
g(1/49) = log (1/7) = -log 7

To find the base of the function F(x) = b^x, we need to use the given point (1/3, 2).

1. Substitute the given x-coordinate (1/3) into the function: F(1/3) = b^(1/3).
2. Set the result equal to the given y-coordinate (2): 2 = b^(1/3).
3. Cube both sides of the equation to isolate b: (2)^3 = (b^(1/3))^3.
This gives us 8 = b.

Therefore, the base of the function F(x) is 8.

Moving on to the next question, if g(x) = log base 7 of x, we are asked to find g(1/49).

1. Substitute the given value (1/49) into the function: g(1/49) = log 7 (1/49).
2. Simplify the expression: g(1/49) = log (1/49) base 7.
3. Then, use the logarithmic identity: log (a/b) base c = log a base c - log b base c.
In this case, log (1/49) base 7 = log 1 base 7 - log 49 base 7.
4. Apply the properties of logarithms: log 1 base 7 is 0 since any number raised to the power of 0 is 1, and log 49 base 7 is 2 since 7^2 = 49.
Therefore, g(1/49) = 0 - 2 = -2.

Hence, g(1/49) equals -2.