Question 51

Find the value of x from the following equation:
$$\log_{10}{3}+\log_{10}(4x+1)=\log_{10}(x+1)+1$$

Solution

$$\log_{10}{3}+\log_{10}(4x+1)=\log_{10}(x+1)+1$$ can be written as

$$\log_{10}{3}+\log_{10}(4x+1)=\log_{10}(x+1)+\log_{10}{10}$$

We know that $$\log_{10}{a}+\log_{10}{b}=\log_{10}{ab}$$

$$\log_{10}{3*(4x+1)}=\log_{10}{(x+1)*10}$$

$$12x+3=10x+10$$

$$x=7/2$$. Hence, option B is the correct answer.

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