How would I solve the equation: log(base2)4 - log(base2)(x+3) = log(base2)8 ?

i think i have to start by doing 4/(x+3)=8

yes, now finish that by cross-multiplying, then solving for x

(you should get x = -5/2)

ok. i got that. thanks for your help. :-)

To solve the equation: log(base2)4 - log(base2)(x+3) = log(base2)8, you can start by using logarithmic properties to simplify the equation.

1. Apply the quotient rule: log(base2)4 - log(base2)(x+3) = log(base2)8
This becomes: log(base2)(4/(x+3)) = log(base2)8

2. Since both sides of the equation have the same logarithmic base, you can eliminate the base and set the expressions inside the logarithms equal to each other.
4/(x+3) = 8

3. Simplify the equation by multiplying both sides by (x+3) to isolate the variable.
4 = 8(x+3)

4. Distribute 8 to each term inside the parentheses.
4 = 8x + 24

5. Move the constant term (24) to the other side of the equation by subtracting it from both sides.
4 - 24 = 8x

6. Simplify the left side of the equation.
-20 = 8x

7. Solve for x by dividing both sides by 8.
-20/8 = x

8. Simplify the right side of the equation.
-2.5 = x

The solution to the equation is x = -2.5.