inverse exponential function help??? ill medal u if u help me out

Question

anonymous · Answer

1. Given the function f(x) = 0.5(3)x, what is the value of f−1(7)?
2. If f(x) = log2 (x + 4), what is f−1(3)?

imer · Answer

Please write equations correctly, I am pretty sure you mean,$$f(x)=0.5(3)^x$$and $$f ^{-1}(7)$$for the first part of the question, correct?

campbell_st · Answer

well start with 

$$y = 0.5 \times 3^x$$

swap x and y, so 

$$x = 0.5 \times 3^y$$

now to find the inverse make y the subject

multiply both sides by 2

$$2x = 3^y$$

take the log of both sides

$$\ln(2x) = \ln(3^y)$$

apply the log law for powers

$$\ln(2x) = ytimes \ln(3)$$

divide both sides of the equation by ln(3)

so 

$$y = \frac{\ln(2x)}{\ln(3)}$$

now substitute x = 7 to find 

$$f^{-1}(7)$$

hope it helps

campbell_st · Answer

Question 2 follows the same process, swap x and y then make y the subject

this will give you the inverse function.