A) 1
B) 3
C) 5
D) 10
Correct Answer: B
Solution :
(b): \[lo{{g}_{10}}5+lo{{g}_{10}}(5x+1)=lo{{g}_{10}}(x+5)+1\] \[\Rightarrow lo{{g}_{10}}5+lo{{g}_{10}}(5x+1)=lo{{g}_{10}}\left[ (x+5) \right]+{{\log }_{10}}10\] \[\Rightarrow lo{{g}_{10}}5+lo{{g}_{10}}(5x+1)=lo{{g}_{10}}\left[ 10(x+5) \right]\] \[\Rightarrow 5(5x+1)=10(x+5)\] \[\Rightarrow 5x+1=2x+10\Rightarrow \,\,\,\,\,3x=9\,\,\,\,\Rightarrow \,\,\,\,x=3.\]
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