Answer to Question #197910 in Algebra for Tavlene Singh

Question

Use rules of logarithms to solve the equation log(3x − 2) − log(2) = log(x + 4) [1] x = −10 [2] x = 10 [3] x = 5 [4] x = 15

Answer 1

Applying the property of the subtraction of logarithms we have:

$$\log (3x-2)-\log (2)=\log (x+4)\Leftrightarrow \log \left( \dfrac{3x-2}{2}\right) =\log (x+4)$$

Then:

$$\dfrac{3x-2}{2}=x+4\Rightarrow 3x-2=2(x+4)\Rightarrow 3x-2=2x+8$$

$$\Rightarrow 3x-2x=8+2\Rightarrow x=10.$$

Therefore, the solution of the equation is $x=10$ .