Question

What is the value of x in the expression log (x+7) - log (x - 7) = log 2?​

Answer 1

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The above question is based upon logarithmic equations where we have to solve for the value of x by using logarithmic properties.

Question:

• log (x + 7) - log (x - 7) = log 2

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By using quotient property of logarithm,

$\boxed{ \sf{ log_{a}(x) - log_{a}(y) = log_{ a }( \dfrac{x}{y} ) }}$

Considering the base is same for both the terms, Then plugging the values in the above property:

➝ $\sf{log( \dfrac{x + 7}{x - 7} ) = log(2)}$

That means,

➝ $\sf{ \dfrac{x + 7}{x - 7} = 2}$

Cross multiplying,

➝ $\sf{x + 7 = 2(x - 7)}$

➝ $\sf{x + 7 = 2x - 14}$

➝ $\sf{2x - x = 14 + 7}$

➝ $\sf{x = 21}$

Thus, the required value of x is 21.