How do you solve ${log}_{2} (x + 2) - {log}_{2} (x) = 8$ $log_2 (x+2) - log_2(x) =8$ ?

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How do you solve ${log}_{2} (x + 2) - {log}_{2} (x) = 8$ $log_2 (x+2) - log_2(x) =8$ ?

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Answer 1 · 2015-09-18T13:55:40

I found: $x = \frac{2}{255} = 0.007843$ $x=2/255=0.007843$

Explanation:

You can use first a rule of the log that says:
$log x - log y = log (\frac{x}{y})$ $logx-logy=log(x/y)$
and get:
${log}_{2} [\frac{x + 2}{x}] = 8$ $log_2[(x+2)/x]=8$
Then you use the definition of log to get:
$\frac{x + 2}{x} = 2^{8}$ $(x+2)/x=2^8$
rearranging:
$x + 2 = 256 x$ $x+2=256x$
$255 x = 2$ $255x=2$
$x = \frac{2}{255} = 0.007843$ $x=2/255=0.007843$

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How do you solve ${log}_{2} (x + 2) - {log}_{2} (x) = 8$ $log_2 (x+2) - log_2(x) =8$ ?

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How do you solve ${log}_{2} (x + 2) - {log}_{2} (x) = 8$ $log_2 (x+2) - log_2(x) =8$ ?