Question

Use the switch and solve meth function: f(x)=2^(3x+1)-6

Answer 1

To solve the function f(x) = 2^(3x+1) - 6 using the switch and solve method, set f(x) equal to zero, add 6 to both sides, take the logarithm (base 2) of both sides, isolate the variable x, and solve for x by dividing both sides by 3.

Step-by-step explanation:

To solve the function f(x) = 2(3x+1) - 6, you can use the switch and solve method. Here's how you can solve it step-by-step:

1. Start with the equation f(x) = 2(3x+1) - 6.
2. Set f(x) equal to zero and solve for x.
3. 2(3x+1) - 6 = 0.
4. Add 6 to both sides of the equation to get 2(3x+1) = 6.
5. Take the logarithm (base 2) of both sides to undo the exponentiated term. This gives you 3x+1 = log2(6).
6. Subtract 1 from both sides to isolate the variable. This gives you 3x = log2(6) - 1.
7. Finally, divide both sides by 3 to solve for x. This gives you x = (log2(6) - 1) / 3.

So, the solution to the function f(x) = 2(3x+1) - 6 is x = (log2(6) - 1) / 3.

Learn more about Solving exponential equations