A) 4
B) -4
C) 1/4
D) not defined
Correct Answer: B
Solution :
(b): \[\text{lo}{{\text{g}}_{10}}2+\text{lo}{{\text{g}}_{10}}\left( 4x+1 \right)=\text{lo}{{\text{g}}_{10}}\left( x+1 \right)+1\] \[\Leftrightarrow \text{lo}{{\text{g}}_{10}}2+\text{lo}{{\text{g}}_{10}}\left( 4x+1 \right)=\text{lo}{{\text{g}}_{10}}\left( x+1 \right)+{{\log }_{10}}10\] \[\Leftrightarrow \text{lo}{{\text{g}}_{10}}\left[ 2\left( 4x+1 \right) \right]=\text{lo}{{\text{g}}_{10}}\left[ 10\left( x+1 \right) \right]\] \[\Leftrightarrow 2\left( 4x+1 \right)=10\left( x+1 \right)\Leftrightarrow 10x+2\] \[=8x+10\Leftrightarrow 2x=-8\Leftrightarrow x=-4\] When it is putting \[x=-4\]than log\[\left( x+1 \right)\] is not defined
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