How do you solve $log (x + 9) - log x = 3$ $log (x + 9) - log x = 3$ ?

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How do you solve $log (x + 9) - log x = 3$ $log (x + 9) - log x = 3$ ?

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Answer 1 · 2016-03-12T15:42:59

Use the log property ${log}_{a} n - {log}_{a} m = {log}_{a} (\frac{n}{m})$ $log_an - log_am = log_a(n/m)$

Explanation:

$log (x + 9) - log (x) = 3$ $log(x + 9) - log(x) = 3$

$log (\frac{x + 9}{x}) = 3$ $log((x + 9)/(x)) = 3$

Since nothing is noted in subscript, the log is in base 10.

$\frac{x + 9}{x} = 10^{3}$ $(x + 9)/x = 10^3$

$\frac{x + 9}{x} = 1000$ $(x + 9)/x = 1000$

We can now solve as a simple linear equation by using the property $\frac{a}{b} = \frac{m}{n} \Rightarrow a \times n = b \times m$ $a/b = m/n => a xx n = b xx m$

$x + 9 = 1000 x$ $x + 9 = 1000x$

$9 = 999 x$ $9 = 999x$

$\frac{9}{999} = x$ $9/999 = x$

$\frac{1}{111} = x$ $1/111 = x$

Hopefully this helps!

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How do you solve $log (x + 9) - log x = 3$ $log (x + 9) - log x = 3$ ?

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