How to Solve for x

log₄ 6 + log₄ (x + 1) = 2    

We can write

log₄ [6 * (x + 1) ]  = 2

In exponential form, we have

4^2   =  6 (x + 1)    simplify

16 = 6x + 6      subtract 6 from both sides

10  = 6x      divide both sides by 6

10/ 6  = x  =   5/3

Solve for x:
(log(6))/(log(4)) + (log(x + 1))/(log(4)) = 2

Rewrite the left hand side by combining fractions. (log(6))/(log(4)) + (log(x + 1))/(log(4)) = (log(6) + log(x + 1))/(log(4)):
(log(6) + log(x + 1))/(log(4)) = 2

Multiply both sides by log(4):
log(6) + log(x + 1) = 2 log(4)

Subtract log(6) from both sides:
log(x + 1) = 2 log(4) - log(6)

2 log(4) - log(6) = log(4^2) + log(1/6) = log(16) + log(1/6) = log(16/6) = log(8/3):
log(x + 1) = log(8/3)

Cancel logarithms by taking exp of both sides:
x + 1 = 8/3

Subtract 1 from both sides:
Answer: | x = 5/3