How do you solve $log (5 + x) - log (x - 3) = log 3$ $log(5+x)-log(x-3)=log3$ ?

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How do you solve $log (5 + x) - log (x - 3) = log 3$ $log(5+x)-log(x-3)=log3$ ?

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Answer 1 · 2015-12-18T22:29:03

$\times x = 7$ $color(white)(xx)x=7$

Explanation:

$\times log (5 + x) - log (x - 3) = log 3$ $color(white)(xx)log(5+x)-log(x-3)=log3$

The quotient of two positive numbers are calculated as difference of their logarithms. Therefore,
$\Rightarrow log (\frac{5 + x}{x - 3}) = log 3$ $=>log((5+x)/(x-3))=log3$
$\Rightarrow \frac{5 + x}{x - 3} = 3$ $=>(5+x)/(x-3)=3$
$\Rightarrow 3 x - 9 = 5 + x$ $=>3x-9=5+x$

$\Rightarrow 3 x - 9 - x + 9 = 5 + x - x + 9$ $=>3x-9color(red)(-x+9)=5+xcolor(red)(-x+9)$
$\Rightarrow \frac{1}{2} \times 2 x = \frac{1}{2} \times 14$ $=>color(red)(1/2xx)2x=color(red)(1/2xx)14$

$\Rightarrow x = 7$ $=>x=7$

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How do you solve $log (5 + x) - log (x - 3) = log 3$ $log(5+x)-log(x-3)=log3$ ?

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How do you solve log(5+x)−log(x−3)=log3log(5+x)-log(x-3)=log3?

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How do you solve $log (5 + x) - log (x - 3) = log 3$ $log(5+x)-log(x-3)=log3$ ?