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 base of x) contains the point (a,3) . What is the value of a?(1 point)
To find the value of a, we need to determine the value of x when f(x) = 3.
Given f(x) = (2/5)^x and f(x) = 0.064 at x = 3, we can set up the following equation:
(2/5)^3 = 0.064
Simplifying the equation:
8/125 = 0.064
Dividing both sides by 8:
1/125 = 0.008
Therefore, we have 1/125 = 0.008.
To find the logarithmic function g(x), we need to rewrite the equation in logarithmic form:
log2/5 (0.008) = x
Solving for x, we can use logarithmic properties to rewrite the equation:
log2/5 (2/5)^3 = x
3 * log2/5 (2/5) = x
Since log2/5 (2/5) = 1, we have:
3 * 1 = x
Therefore, x = 3.
So, the corresponding logarithmic function g(x) contains the point (a, 3), where a = 3.