To solve this equation, we first need to combine the logarithms using the quotient rule.
log4((x+3)/(x-1)) = 2
Now, we can rewrite the equation in exponential form:
4^2 = (x+3)/(x-1)
16 = (x+3)/(x-1)
Next, we can cross multiply to solve for x:
16(x-1) = x + 3
16x - 16 = x + 3
Subtract x from both sides:
15x - 16 = 3
Add 16 to both sides:
15x = 19
Finally, divide by 15 to solve for x:
x = 19/15
Therefore, the solution to the equation Log4(x+3)-log4(x-1)=2 is x = 19/15.
To solve this equation, we first need to combine the logarithms using the quotient rule.
log4((x+3)/(x-1)) = 2
Now, we can rewrite the equation in exponential form:
4^2 = (x+3)/(x-1)
16 = (x+3)/(x-1)
Next, we can cross multiply to solve for x:
16(x-1) = x + 3
16x - 16 = x + 3
Subtract x from both sides:
15x - 16 = 3
Add 16 to both sides:
15x = 19
Finally, divide by 15 to solve for x:
x = 19/15
Therefore, the solution to the equation Log4(x+3)-log4(x-1)=2 is x = 19/15.