How do you calculate ${log}_{4} 1558$ $log_4 1558$ ?

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Answer 1 · 2016-07-06T21:54:16

Using a calculator: $x = 5.3027$ $x = 5.3027$

If ${log}_{4} 1558 = x, then 4^{x} = 1558$ $log_4 1558 = x, " then " 4^x = 1558$

1558 is not a power of 4 (it is not divisible by 4) so use logs.

Take logs of both sides:

$x log 4 = log 1558$ $xlog4 = log 1558$

$x = \frac{log 1558}{log 4}$ $x = log 1558/log4$

We would get to the same result from the change of base law.

Using a calculator: $x = 5.3027$ $x = 5.3027$

How do you calculate log41558log_4 1558 ?