Log4(6x+7)=3

To solve log₄(6x + 7) = 3, follow these steps:

1. Write the logarithmic equation in its exponential form:
  6x + 7 = 4³

2. Calculate 4³:
  4³ = 64

3. Set up the equation:
  6x + 7 = 64

4. Solve for x:
  6x = 64 − 7
  6x = 57
  x = 57/6
  x = 19/2

So, the solution is x = 19/2.

Remember to check that the argument of the logarithm is positive:
  6(19/2) + 7 = 57 + 7 = 64, which is positive.

Thus, the solution x = 19/2 is valid.