Log(3x+8)-3log2=log(x-4)

Answer 1

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.