How do you calculate ${log}_{6} 53$ $log_6 53$ with a calculator?

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Answer 1 · 2016-08-19T11:01:20

$x = 2.216$ $x = 2.216$

Some calculators can do log calculations with bases other than 10.
However, let's assume that we have a calculator which only has log with base 10.

Let ${log}_{6} 53 = x write in index form$ $log_6 53 = x" write in index form"$

$6^{x} = 53 find log of both sides$ $6^x = 53" find log of both sides"$

${log 6}^{x} = log 53$ $log6^x = log53$

$x log 6 = log 53$ $xlog6 = log53$

$x = \frac{{log}_{10} 53}{{log}_{10} 6}$ $x = log_10 53/log_10 6$

This is the same result as using the change of base rule.

$x = 2.216$ $x = 2.216$

How do you calculate log653log_6 53 with a calculator?