- 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.
