Question

Розв'язати рівняння 2^х-2+2^х=10

Answer 1

2*2^x -2 =10
2^(x+1) = 10+2
2^(x+1) = 12
x+1 = log (2) 12
x = (log(2) 12) -1

x = log(2)(4*3) -1

x = log(2)2² + log(2)3 -1

x = 2+ log(2)3 -1
x = 1 + log(2)3

Answer 2

2^x/4 +2^x=10

2^x=t

t/4+t=10
t+4t=40
5t=40
t=40:5
t=8
2^x=8
2^x=2^3
x=3

Answer 3

I can understand and communicate in Ukrainian. I will try to help you solve the equation.

The equation 2^x - 2 + 2^x = 10 can be rewritten as 2^(x+1) - 2 = 10, by using the property of exponents that a^x * a^y = a^(x+y). Then, we can add 2 to both sides and get 2^(x+1) = 12. Taking the logarithm of both sides with base 2, we get x + 1 = log_2(12), where log_2 is the logarithm function with base 2. Subtracting 1 from both sides, we get x = log_2(12) - 1. This is the exact solution of the equation.

To find an approximate value of x, we can use a calculator or a web tool. The value of log_2(12) is about 3.585, so x is about 3.585 - 1 = 2.585. This means that 2^x - 2 + 2^x is approximately equal to 10 when x is 2.585.

I hope this explanation was helpful. If you want to learn more about exponential equations, you can check out some online resources. You can also practice solving similar equations with online exercises. Have a nice day!