 # Ex: Evaluate Common Logarithms on the Calculator

– WE WANT TO EVALUATE
EACH LOGARITHM ON A CALCULATOR. THEN WRITE
A EXPONENTIAL EQUATION TO SHOW THE MEANING
OF THE VALUE. NOTICE IN BOTH
OF THESE LOGARITHMS THE BASE IS NOT GIVEN THEREFORE WE KNOW IT’S A COMMON
LOGARITHM OR LOG BASE 10. MOST CALCULATORS
ONLY CONTAIN TWO LOG BUTTONS, LOG FOR COMMON LOG AND LN
FOR NATURAL LOG OR LOG BASE E. SO TO EVALUATE THIS FIRST
LOGARITHM WE JUST PRESS LOG, AND BECAUSE THIS COMMON LOG WE
ALREADY KNOW IT’S LOG BASE 10. SO WE JUST TYPE IN 10,000, CLOSE
PARENTHESIS AND PRESS ENTER. THIS IS EQUAL TO 4. SO THIS IS THE FIRST PART
OF THE QUESTION. THE SECOND PART IS WE WANT
TO WRITE AN EXPONENTIAL EQUATION TO EXPLAIN WHY THIS IS EQUAL
TO 4. WELL THE REASON IT’S EQUAL TO 4 IS BECAUSE OUR BASE 10
RAISED TO THE 4th POWER IS EQUAL TO 10,000. SO THIS EMPHASIS’S THAT
WHEN WE EVALUATE A LOGARITHM, WE’RE ACTUALLY FINDING
AN EXPONENT AND IN THIS CASE,
IT’S TELLING US THAT 10 TO THE 4th
IS EQUAL TO 10,000. NOW WE HAVE THE COMMON LOG
OF 1/10, SO WE’LL GO BACK TO THE
CALCULATOR AND PRESS THE LOG KEY WHICH IS THE COMMON LOG
AND THEN 1/10, SO 1 DIVIDED BY 10, CLOSES
PARENTHESIS, AND PRESS ENTER. THIS IS EQUAL TO -1. AND AGAIN, TO SHOW
WHY THIS IS EQUAL TO -1, WE CAN WRITE
AN EXPONENTIAL EQUATION. SO WE’D HAVE THE BASE 10
RAISED TO THE -1 POWER IS EQUAL TO THE NUMBER OF 1/10. AGAIN, THIS EMPHASIS’S WHEN WE DETERMINE THE VALUE
OF A LOGARITHM WE’RE ACTUALLY FINDING
AN EXPONENT. IN THIS CASE, 10 TO THE -1 POWER
IS EQUAL TO 1/10.