To solve the first equation, we can rewrite it as:

x + 7 = 6x - 13

Solving for x, we get:

7 + 13 = 6x - x
20 = 5x
x = 4

Therefore, the solution for the first equation is x = 4.

For the second equation, we can rewrite it as:

log2(8 + 3x) = log2(3 - x) + 1

Using the rule of logarithms where log_a(x) = log_a(y) is equivalent to x = y, we can rewrite the equation as:

8 + 3x = 2^(3 - x + 1)

8 + 3x = 2^3 * 2^(-x)
8 + 3x = 8 / 2^x

Solving for x, we get:

8 + 3x = 8 / 2^x
3x = 8 / 2^x - 8
3x = 8(1 - 2^(-x))
x = 8 / 3(1 - 2^(-x))

Therefore, the solution for the second equation is x = 8 / 3*(1 - 2^(-x)).