We can simplify the equation using the properties of logarithms:
log5(x+3) + log1/5(x+4) = log5(5)log5[(x+3)(x+4)] = log5(5)
Since the logarithms on both sides are equal, we can set the expressions inside the logarithms equal to each other:
(x+3)(x+4) = 5
Expanding the left side of the equation:
x^2 + 4x + 3x + 12 = 5x^2 + 7x + 12 = 5x^2 + 7x + 7 = 0
Now we have a quadratic equation that we can solve by factoring or using the quadratic formula:
(x+7)(x+1) = 0
This gives us two possible solutions:
x+7 = 0x = -7
x+1 = 0x = -1
So the solutions to the equation are x = -7 and x = -1.
We can simplify the equation using the properties of logarithms:
log5(x+3) + log1/5(x+4) = log5(5)
log5[(x+3)(x+4)] = log5(5)
Since the logarithms on both sides are equal, we can set the expressions inside the logarithms equal to each other:
(x+3)(x+4) = 5
Expanding the left side of the equation:
x^2 + 4x + 3x + 12 = 5
x^2 + 7x + 12 = 5
x^2 + 7x + 7 = 0
Now we have a quadratic equation that we can solve by factoring or using the quadratic formula:
(x+7)(x+1) = 0
This gives us two possible solutions:
x+7 = 0
x = -7
x+1 = 0
x = -1
So the solutions to the equation are x = -7 and x = -1.