Question

2\5^cosx + 5\2^cosx = 2

Answer 1

4/10^cosx+25/10^cosx=2
cosx+cosx=2
2cosx=2
cosx=1
x=0+2пn, n-целое

Answer 2

To solve the equation $2\cdot5^{\cos(x)} + 5\cdot2^{\cos(x)} = 2$, we can start by simplifying it a bit. Notice that both terms have a common factor of 2, so we can factor that out:

$2(5^{\cos(x)} + 2^{\cos(x)}) = 2.$

Now, divide both sides of the equation by 2:

$5^{\cos(x)} + 2^{\cos(x)} = 1.$

Now, we want to isolate the term with $2^{\cos(x)}$, so subtract $5^{\cos(x)}$ from both sides:

$2^{\cos(x)} = 1 - 5^{\cos(x)}.$

Next, we'll take the natural logarithm (ln) of both sides to get rid of the exponent:

$\ln(2^{\cos(x)}) = \ln(1 - 5^{\cos(x)}).$

Now, we can use the property of logarithms that allows us to bring the exponent down as a coefficient:

$\cos(x) \ln(2) = \ln(1 - 5^{\cos(x)}).$

Finally, divide both sides by $\ln(2)$ to solve for $\cos(x)$:

$\cos(x) = \frac{\ln(1 - 5^{\cos(x)})}{\ln(2)}.$

This is a transcendental equation, and solving it for $\cos(x)$ directly is not straightforward. You may need to use numerical methods or approximation techniques to find an approximate solution for $\cos(x)$.