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Question #3629d

1 Answer

Dec 20, 2016

There is no solution in the real number system.

Explanation:

Rewrite as a single logarithm using the rule ${log}_{a} n - {log}_{a} m = {log}_{a} (\frac{n}{m})$ $color(magenta)(log_a n - log_a m = log_a (n/m)$

$log (\frac{x + 1}{x}) = 0$ $log((x+ 1)/x) = 0$

Convert to exponential form; the notation $log x = a$ $logx = a$ is equivalent to $x = 10^{a}$ $x = 10^a$ in exponential form.

$\frac{x + 1}{x} = 10^{0}$ $(x + 1)/x = 10^0$

$\frac{x + 1}{x} = 1$ $(x + 1)/x = 1$

$x + 1 = x$ $x + 1 = x$

$1 = 0 x$ $1 = 0x$

$x = \frac{1}{0}$ $x = 1/0$

$x = \emptyset$ $x = O/$

Hopefully this helps!

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