Log4(6x+7)=3

We start with the equation:
  log₄(6x + 7) = 3

To solve for x, rewrite the logarithmic equation in exponential form. Recall that if logₐ(b) = c, then aᶜ = b. Applying this gives:
  6x + 7 = 4³

Since 4³ = 64, the equation becomes:
  6x + 7 = 64

Now, subtract 7 from both sides:
  6x = 64 − 7
  6x = 57

Finally, divide both sides by 6:
  x = 57 / 6
  x = 19 / 2

Thus, the solution is:
  x = 19/2

Always check the solution by substituting back into the original equation to ensure it is valid.