Log(3x+8)-3log2=log(x-4)
To solve the equation log(3x+8) - 3log2 = log(x-4), we can use logarithmic properties to simplify the equation.
First, we can use the rule log(a)-log(b) = log(a/b) to combine the logarithms on the left side of the equation:
log(3x+8) - log(2^3) = log(x-4)
Using the rule log(a^n) = nlog(a), we can simplify further:
log(3x+8) - log(8) = log(x-4)
Now, using the rule log(a)-log(b) = log(a/b) again, we have:
log((3x+8)/8) = log(x-4)
Since the logarithms are equal, the expressions inside the logarithms must also be equal:
(3x+8)/8 = x-4
Now, let's solve for x:
3x + 8 = 8(x - 4)
Distribute the 8 on the right side:
3x + 8 = 8x - 32
Subtract 3x from both sides:
8 = 5x - 32
Add 32 to both sides:
40 = 5x
Divide both sides by 5:
8 = x
So the solution to the equation log(3x+8) - 3log2 = log(x-4) is x = 8.
To solve the equation log(3x+8) - 3log(2) = log(x-4), we will use logarithmic properties to simplify the equation and then solve for x.
Step 1: Apply the logarithmic property log(a) - log(b) = log(a/b) to simplify the left side of the equation.
log(3x+8) - 3log(2) = log(x-4)
log((3x+8)/(2^3)) = log(x-4)
Step 2: Simplify the logarithmic expression.
log((3x+8)/8) = log(x-4)
Step 3: Set the argument of the logarithm on both sides of the equation equal to each other.
(3x+8)/8 = x-4
Step 4: Multiply both sides of the equation by 8 to eliminate the denominator.
3x + 8 = 8(x-4)
Step 5: Distribute the 8 on the right side of the equation.
3x + 8 = 8x - 32
Step 6: Combine like terms.
3x - 8x = -32 - 8
-5x = -40
Step 7: Divide both sides of the equation by -5 to solve for x.
x = (-40)/(-5)
x = 8
Therefore, the solution to the equation log(3x+8) - 3log(2) = log(x-4) is x = 8.