How do you solve ${log}_{4} 5 - {log}_{4} x = {log}_{4} (\frac{5}{4})$ $log_4 5 - log_4x = log_4(5/4)$ ?

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Answer 1 · 2016-10-06T18:20:07

$x = 4$ $x=4$

${log}_{4} 5 - {log}_{4} x = {log}_{4} (\frac{5}{4})$ $log_4 5 - log_4x = log_4(5/4)$

Condense two log terms into one log term
$\to$ $rarr$ If the logs are being subtracted, the values are being divided.

${log}_{4} (\frac{5}{x}) = {log}_{4} (\frac{5}{4})$ $log_4(5/x) = log_4(5/4)$

Without any further working, we can see by inspection that

$x = 4$ $x=4$

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