How do you calculate ${log}_{6} 73$ $log_6 73$ with a calculator?

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Answer 1 · 2016-08-31T11:18:27

$x = 2.395$ $x = 2.395$

Log form and index form are interchangeable.

${log}_{a} b = c \Leftrightarrow a^{c} = b$ $log_a b = c hArr a^c = b$

Let ${log}_{6} 73 = x \Leftrightarrow 6^{x} = 73$ $log_6 73 = x hArr 6^x = 73$

The variable is in the index, so we need logs.

${log 6}^{x} = log 73$ $log6^x = log73$

$x log 6 = log 73$ $x log6 = log73$

$x = \frac{log 73}{log 6}$ $x = log73/log6$

$x = 2.395$ $x = 2.395$

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