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