Question

2^(x+3)-5*2^(x)=3*2^(-1)

Answer 1

2^x(2^3 - 5) = 1.5
2^x=1.5/3
2^x=0.5
2^x=2^-1
x=-1

Answer 2

To solve for x in the equation:

2^(x+3) - 52^x = 32^(-1)

We can start by using exponent rules to simplify the left-hand side of the equation:

2^(x+3) can be written as 2^x * 2^3 = 8*2^x

Substituting this in, we get:

82^x - 52^x = 3*2^(-1)

Simplifying further, we get:

32^x = 32^(-1)

Dividing both sides by 3, we get:

2^x = 2^(-1)

Now, we can solve for x by taking the logarithm of both sides with base 2:

x = -1

Therefore, the solution to the equation is x = -1.