Question

Хееееееееееееелп 5^х=√5

Answer 1

${5}^{x} = \sqrt{5}$
${5}^{x} = {5}^{ \frac{1}{2} }$
$x = \frac{1}{2}$

Answer 2

Что значит галочка на верху

Answer 3

Sure, I'd be happy to help you solve the equation $5^x = \sqrt{5}$.

To solve for $x$, we can use logarithms. Specifically, take the natural logarithm (base $e$) of both sides of the equation:

$\ln(5^x) = \ln(\sqrt{5})$

Now, we can use the properties of logarithms to simplify the equation. The property we'll use here is $\ln(a^b) = b \cdot \ln(a)$:

$x \cdot \ln(5) = \ln(\sqrt{5})$

Next, we can isolate $x$ by dividing both sides of the equation by $\ln(5)$:

$x = \frac{\ln(\sqrt{5})}{\ln(5)}$

Now, we need to evaluate the right-hand side of the equation. The natural logarithm of a number is the exponent to which the base $e$ must be raised to obtain that number. So, $\ln(\sqrt{5})$ is the exponent to which $e$ must be raised to get $\sqrt{5}$:

$\ln(\sqrt{5}) = \frac{1}{2} \cdot \ln(5)$

Substitute this back into the equation for $x$:

$x = \frac{\frac{1}{2} \cdot \ln(5)}{\ln(5)}$

Now, the $\ln(5)$ terms cancel out:

$x = \frac{1}{2}$

So, the solution to the equation $5^x = \sqrt{5}$ is $x = \frac{1}{2}$.