If $${\log _5}\left( {{x^2} + x} \right) - $$ $${\log _5}\left( {x + 1} \right)$$ = 2, then the value of x is -
A. 5
B. 10
C. 25
D. 32
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\log _5}\left( {{x^2} + x} \right) - {\log _5}\left( {x + 1} \right) = 2 \cr & \Rightarrow {\log _5}\left( {\frac{{{x^2} + x}}{{x + 1}}} \right) = 2\, \cr & \Rightarrow {\log _5}\left[ {\frac{{x\left( {x + 1} \right)}}{{x + 1}}} \right] = 2 \cr & \Rightarrow {\log _5}x = 2 \cr & \Rightarrow x = {5^2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 25 \cr} $$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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