If $${\log _{10}}5 + {\log _{10}}\left( {5x + 1} \right)$$ = $${\log _{10}}$$ $$\left( {x + 5} \right)$$ $$\, + $$ $$1,$$ then x is equal to :
A. 1
B. 3
C. 5
D. 10
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & \Rightarrow {\log _{10}}5 + {\log _{10}}\left( {5x + 1} \right) = {\log _{10}}\left( {x + 5} \right) + 1 \cr & \Rightarrow {\log _{10}}\left[ {5\left( {5x + 1} \right)} \right] = {\log _{10}}\left[ {10\left( {x + 5} \right)} \right] \cr & \Rightarrow 5\left( {5x + 1} \right) = 10\left( {x + 5} \right) \cr & \Rightarrow 5x + 1 = 2x + 10 \cr & \Rightarrow 3x = 9 \cr & \Rightarrow x = 3 \cr} $$Related Questions on Logarithm
Which of the following statements is not correct?
A. log10 10 = 1
B. log (2 + 3) = log (2 x 3)
C. log10 1 = 0
D. log (1 + 2 + 3) = log 1 + log 2 + log 3
$${{\log \sqrt 8 } \over {\log 8}}$$ is equal to:
A. $$\frac{1}{6}$$
B. $$\frac{1}{4}$$
C. $$\frac{1}{2}$$
D. $$\frac{1}{8}$$
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