How do you calculate #log_5 (-28)# with a calculator?

1 Answer
Sep 26, 2016

Answer:

See explanation.

Explanation:

The given logarythm cannot be calculated because #log# is only defined for positive values, but there is a procedure of calculating any legal logatrythm using a calculator.

To do this we have to use the Change of Base Formula, which is:

#log_ax=log_bx/log_ba#

This formula lets us change the logarythm with non standard base to a quotient of logarythms of any other base.

Calculators don't have logarythm of base #5#, but they usually have either natural logarythm #ln# or base 10 logarythm #log#. I will explain the procedure using base #10#.

The procedure is:

  1. Press #5# and #log# to calculate #log5#.

  2. Press #M# to put the result in memory.

  3. Press #28# and #log# to display #log28#

  4. Press #-:# (division) button

  5. Press #RM# to recall the result stored in pt. 2.

  6. Press #=# to calculate the final result.