Final Answer:
The solution to the equation e^(2x) = 2/7 is x = ln(2/7)/2.
Step-by-step explanation:
To find the solution to the given equation, e^(2x) = 2/7, we can start by taking the natural logarithm (ln) of both sides to eliminate the exponential term.
2x * ln(e) = ln(2/7)
Since ln(e) is equal to 1, we have:
2x = ln(2/7)
Now, we can isolate x by dividing both sides by 2:
x = ln(2/7)/2
Thus, the solution to the equation is x = ln(2/7)/2.
In conclusion, by applying the natural logarithm to both sides and simplifying using logarithmic properties, we find that x is equal to ln(2/7)/2. This represents the solution to the given exponential equation. It's essential to understand the properties of logarithms and exponentials to manipulate the equation correctly and arrive at the final solution.