Solve for x :
log (x + 4) − log (x − 4) = log 2
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Given,
⇒log (x+4)−log (x−4)=log 2⇒log (x+4)(x−4)=log 2⇒(x+4)(x−4)=2⇒(x+4)=(x−4)×2⇒x+4=2x−8⇒2x−x=8+4⇒x=12.\Rightarrow \log \space (x + 4) - \log \space (x - 4) = \log \space 2 \\[1em] \Rightarrow \log \space \dfrac{(x + 4)}{(x - 4)} = \log \space 2 \\[1em] \Rightarrow \dfrac{(x + 4)}{(x - 4)} = 2 \\[1em] \Rightarrow (x + 4) = (x - 4) \times 2 \\[1em] \Rightarrow x + 4 = 2x - 8 \\[1em] \Rightarrow 2x - x = 8 + 4 \\[1em] \Rightarrow x = 12 .⇒log (x+4)−log (x−4)=log 2⇒log (x−4)(x+4)=log 2⇒(x−4)(x+4)=2⇒(x+4)=(x−4)×2⇒x+4=2x−8⇒2x−x=8+4⇒x=12.
Hence, the value of x = 12.
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If log (a+b2)=12(log a+log b) , show that 12(a+b)=ab\log \space \Big(\dfrac{a + b}{2}\Big) = \dfrac{1}{2} (\log \space a + \log \space b)\text{ , show that }\dfrac{1}{2} (a + b) = \sqrt{ab}log (2a+b)=21(log a+log b) , show that 21(a+b)=ab.
log (x + 2) + log (x − 2) = log 5
log (x + 3) − log (x − 3) = 1
log (x2 − 21) = 2
