Answer to Question #197910 in Algebra for Tavlene Singh

Question #197910

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


1
Expert's answer
2021-06-01T07:57:33-0400

Applying the property of the subtraction of logarithms we have:


log(3x2)log(2)=log(x+4)log(3x22)=log(x+4)\log (3x-2)-\log (2)=\log (x+4)\Leftrightarrow \log \left( \dfrac{3x-2}{2}\right) =\log (x+4)

Then:


3x22=x+43x2=2(x+4)3x2=2x+8\dfrac{3x-2}{2}=x+4\Rightarrow 3x-2=2(x+4)\Rightarrow 3x-2=2x+8

3x2x=8+2x=10.\Rightarrow 3x-2x=8+2\Rightarrow x=10.

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


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