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

1 Answer
Sep 26, 2016

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.