#1**+1 **

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**

Guest Apr 4, 2017