Question

Знайти корінь рівняння 0,5^x=0,25

Answer 1

(5/10)^x=25/100
(5/10)^x=(5/10)^2
x=2

Answer 2

I can help you with your math problem. To find the root of the equation $0.5^x=0.25$, you need to use the logarithm function. The logarithm of a number is the power to which a base must be raised to produce that number. For example, $\log_2 8 = 3$ because $2^3 = 8$.

Using this property, you can rewrite the equation as $\log_{0.5} 0.25 = x$. Then, you can use the change of base formula to convert the logarithm to a different base, such as 10 or e. The formula is $\log_b a = \frac{\log_c a}{\log_c b}$, where $c$ is any valid base. For example, $\log_{0.5} 0.25 = \frac{\log_{10} 0.25}{\log_{10} 0.5}$.

Now, you can use a calculator to evaluate the logarithms and get the value of $x$. The answer is $x \approx 1.000$. You can check your answer by plugging it back into the original equation and see if it is true.

For more information on logarithms and how to solve exponential equations, you can visit these websites: [Online calculator. Solving quadratic equations](https://ua.onlinemschool.com/math/assistance/equation/quadratic/), [Root Calculator - Symbolab](https://ru.symbolab.com/solver/roots-calculator), [Square root calculator - OnlineMSchool](https://ua.onlinemschool.com/math/assistance/number_theory/square-root-calculator/). I hope this helps. Have a nice day.