How do you calculate $log_7 5.8$ with a calculator?

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Answer 1 · 2016-08-09T08:25:39

$log_7 5.8 = (log_10 5.8)/(log_10 7) = 0.9034$

Some calculators are able to calculate logs with any base, but let's work through this for those calculators which can only work with base 10.

Let $log_7 5.8 = x" log form"$

$7^x = 5.8" index form"$

The variable is in the index, find the log of both sides.

$log_10 7^x = log_10 5.8$

$xlog_10 7 = log_10 5.8$

$x = (log_10 5.8)/(log_10 7)$

Now use a calculator to find the answer $0.9034$

$log_a b = (log_10 b)/(log_10 a) " is called the change of base law"$

We could have written the following in one step:

$log_7 5.8 = (log_10 5.8)/(log_10 7)$

How do you calculate log_7 5.8log_7 5.8 with a calculator?