How do you evaluate ${log}_{3} (\frac{1}{243})$ $log_3 (1/243)$ ?

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Answer 1 · 2016-10-01T13:46:36

${log}_{3} (\frac{1}{243}) = {log}_{3} 3^{- 5} = - 5$ $log_3 (1/243) = log_3 3^-5 = -5$

Logs and exponential equations become much easier to understand if you know the powers up to 1,00.

Note that $243 = 3^{5}$ $243 = 3^5$

${log}_{3} (\frac{1}{243})$ $log_3 (1/243)$ is asking the question..

$What index of 3 gives \frac{1}{243}$ $"What index of 3 gives "1/243$ ?

$\frac{1}{243} is which power of 3$ $1/243 " is which power of " 3$ ?

$\frac{1}{243} = \frac{1}{3^{5}} = 3^{- 5} \leftarrow$ $1/243 = 1/3^5 = 3^-5" "larr$ here is our answer!

${log}_{3} (\frac{1}{243}) = {log}_{3} 3^{- 5} = - 5$ $log_3 (1/243) = log_3 3^-5 = -5$

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