How do you solve $2 log x = log 25 + 2$ $2 log x = log 25 + 2$ ?

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How do you solve $2 log x = log 25 + 2$ $2 log x = log 25 + 2$ ?

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Answer 1 · 2015-12-29T13:45:22

Use the fact that $log (x)$ $log(x)$ is a one-one function as a Real-valued function of Real numbers to find:

$x = 50$ $x = 50$

Explanation:

Divide both sides by $2$ $2$ to get:

$log (x)$ $log(x)$

$= \frac{log (25) + 2}{2}$ $= (log(25)+2) / 2$

$= \frac{2 log (5) + 2 log (10)}{2}$ $= (2 log(5) + 2 log(10))/2$

$= log (5) + log (10)$ $= log(5) + log(10)$

$= log (50)$ $= log(50)$

Hence $x = 50$ $x = 50$ , since $log(x):(0, oo) -> RR$ is one-one.

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How do you solve $2 log x = log 25 + 2$ $2 log x = log 25 + 2$ ?

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