find the inverse of log5(2x+1)=g(x)
Is that log to base 5 or log [5(2x+1)] ?
Assuming that you mean base 5,
5^g = 2x +1
x = [5^g -1]/2
which can be written,
g^-1(x) = [5^g -1]/2
where g^-1(x) is the inverse function of g(x)
To find the inverse of the function log5(2x+1) = g(x), we need to solve for x.
Step 1: Start by expressing the equation in exponential form. The logarithmic equation log5(2x+1) = g(x) is equivalent to the exponential equation 5^g(x) = 2x+1.
Step 2: Solve the exponential equation for x. Rewrite the equation as 2x+1 = 5^g(x) and isolate x.
2x = 5^g(x) - 1
x = (5^g(x) - 1)/2
Therefore, the inverse of the function log5(2x+1) = g(x) is x = (5^g(x) - 1)/2.