An exponential function f(x)=(2/5)^x contains the point (3,0.064) . Its corresponding logarithmic function g(x)=log2/5 x (2/5 is the log base of x) contains the point (a,3) . What is the value of a?(1 point)

Answer 1

To find the value of a, we need to determine the x-coordinate of the point (a, 3) on the logarithmic function g(x) = log2/5(x).

We know that the point (3, 0.064) lies on the exponential function f(x) = (2/5)^x. This means that when x = 3, f(x) = 0.064.

Substituting these values into the exponential function, we have:
0.064 = (2/5)^3

To simplify, we can rewrite (2/5)^3 as (2^3)/(5^3):
0.064 = (8)/(125)

Now, let's solve for the value of x in the logarithmic function g(x) = log2/5(x) when y = 3:
3 = log2/5(a)

Exponentiating both sides with a base of 2/5, we get:
(2/5)^3 = a

So, a = (2/5)^3 = 8/125

The value of a is 8/125.