solve the following exponential equation. use exact answers only.
not sure how to put it into the equation but it is 2 then 1-9x where the 1-9x is above the 2=e2x where the 2x is above the 2.
Can someone tell me or explain to me how to put this equation the right way here.
. 4(x-3) = 5(x+1) Solve the equation above for x. Which of the following is correct?
A. -17
B. -4
C. 4
D. 17
To properly format the equation, it seems like you are looking to solve the exponential equation:
2^(1-9x) = e^(2x)
To solve this equation, we need to transform it into a common base. Since both sides are in exponential form, we can solve it using the natural logarithm (ln). Here's how:
1. Take the natural logarithm (ln) of both sides of the equation:
ln(2^(1-9x)) = ln(e^(2x))
2. Apply the logarithmic property to bring down the exponents:
(1-9x) ln(2) = 2x ln(e)
3. Simplify using the fact that ln(e) = 1:
(1-9x) ln(2) = 2x
4. Distribute ln(2) into the parentheses:
ln(2) - 9x ln(2) = 2x
5. Rearrange the equation so that all the x terms are on one side:
-9x ln(2) - 2x = -ln(2)
6. Factor out x:
x (-9ln(2) - 2) = -ln(2)
7. Divide both sides by (-9ln(2) - 2) to isolate x:
x = -ln(2) / (-9ln(2) - 2)
This is the exact solution to the exponential equation.