I am trying to find the inverse of these functions. Can someone please check my answers and tell me how to do number 2?

1. y=7^x
y=log base 7 x

2. y=log base 1/2 x

3. y=2^(x)-3
y=2^(x+3)

4.y=6+log x

#1. ok

#2. y = (1/2)x = 2-x
#3. log2(x+3)
#4. e^(x-6)
if base 10, 10^(x-6)

Thank you

1 ok

2. b^logb(x) = x
x = log.5 y
.5^x = .5^log.5(y) = y
so
y = .5^x

3. x = 2^y - 3
x+3 = 2^y
log2 (x+3) = y

4. x = 6 + log y log base e or 10 ???
I will assume 10
x-6 = log y
10^(x-6) = y
y = 10^x/10^6

Sure, I can help you with that! Let's go through each function one by one and check your answers:

1. To find the inverse of the function y = 7^x, you can follow these steps:
- Start by replacing the y with x and the x with y: x = 7^y
- Next, take the logarithm of both sides of the equation: log base 7 (x) = y
- Therefore, the inverse function is y = log base 7 (x)

2. Now, let's find the inverse of the function y = log base (1/2) x.
- Start as we did before by replacing the y with x and the x with y: x = log base (1/2) y
- Now, in order to solve for y, we need to convert the logarithmic equation into an exponential form.
- The logarithmic equation log base (a) b = c can be written as a^c = b.
- Applying this to our equation, we have (1/2)^x = y.
- Therefore, the inverse function is y = (1/2)^x.

3. To find the inverse of the function y = 2^(x) - 3, follow these steps:
- Replace the y with x and the x with y: x = 2^(y) - 3
- Add 3 to both sides of the equation: x + 3 = 2^(y)
- Next, take the logarithm of both sides of the equation to solve for y: log base 2 (x + 3) = y
- Therefore, the inverse function is y = log base 2 (x + 3)

4. Lastly, to find the inverse of the function y = 6 + log x, follow these steps:
- Replace the y with x and the x with y: x = 6 + log y
- Subtract 6 from both sides of the equation: x - 6 = log y
- To solve for y, we need to convert the logarithmic equation into an exponential form.
- The logarithmic equation log base (a) b = c can be written as a^c = b.
- Applying this to our equation, we have 10^(x - 6) = y.
- Therefore, the inverse function is y = 10^(x - 6).

These are the correct inverse functions for each of the given functions. I hope this helps! Let me know if you have any further questions.