Question

Evaluate without using a calculator or math table:log(3x+8)-3log2=log(x-4)

Answer 1

To solve for x in the equation log(3x+8) - 3log(2) = log(x-4), we can use the properties of logarithms:

1. Simplify the equation:
log(3x+8) - log(2^3) = log(x-4)
log(3x+8) - log(8) = log(x-4)

2. Combine the logarithms:
log((3x+8)/8) = log(x-4)

3. Remove the logarithms by equating the expressions inside the logarithms:
(3x+8)/8 = x-4

4. Simplify the equation:
3x+8 = 8(x-4)

5. Distribute on the right side of the equation:
3x+8 = 8x-32

6. Move all the terms containing x to one side and the constants to the other side:
3x - 8x = -32 - 8
-5x = -40

7. Divide both sides of the equation by -5:
x = (-40)/(-5)

8. Simplify:
x = 8

Therefore, the solution to the equation log(3x+8) - 3log(2) = log(x-4) is x = 8.