#solving a challenging exponential equation (vid16)

After watching this video, you would be able to solve challenging exponential equations.
Exponential Equation
Example
Solve for x: 2^(x+1) = 3^(2x-1)

Steps
1. Take the logarithm of both sides (base 10 or natural logarithm).
2. Apply logarithmic properties to simplify.
3. Isolate x.

Solution
Let's use natural logarithms:

1. ln(2^(x+1)) = ln(3^(2x-1))
2. (x+1)ln(2) = (2x-1)ln(3)
3. Expand and solve for x:
xln(2) + ln(2) = 2xln(3) - ln(3)
xln(2) - 2xln(3) = -ln(3) - ln(2)
x(ln(2) - 2ln(3)) = -ln(3) - ln(2)
x = (-ln(3) - ln(2)) / (ln(2) - 2ln(3))

Tips
1. _Choose a suitable logarithm base_: Base 10 or natural logarithm.
2. _Apply logarithmic properties_: Use properties like ln(a^b) = b × ln(a).

Would you like more examples or practice problems?
how to #solve an #exponential #equation.

Видео #solving a challenging exponential equation (vid16) канала Understanding Mathematics with Pride