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- ONE APPLICATION OF A LOG FUNCTION IS THE PH SCALE.
THE PH SCALE MEASURES THE ACIDITY OF A SUBSTANCE
AND IS DEFINED BY PH EQUALS
NEGATIVE THE COMMON LOG OF THE CONCENTRATION OF HYDROGEN IONS
MEASURED IN MOLES PER LITER.
SO IF A SAMPLE OF MILK HAS A HYDROGEN CONCENTRATION
OF APPROXIMATELY 0.0000125 MOLES PER LITER
WE CAN FIND THE PH BY SUBSTITUTING THIS VALUE
IN FOR THE HYDROGEN ION CONCENTRATION.
SO THE PH OF THIS MILK WOULD BE EQUAL TO
THE OPPOSITE OR NEGATIVE COMMON LOG OF 0.0000125.
AND NOW WE'LL USE THE CALCULATOR TO APPROXIMATE THE PH.
SO WE'LL JUST TYPE IN NEGATIVE COMMON LOG
AND THEN THE HYDROGEN ION CONCENTRATION.
SO THE PH WOULD BE APPROXIMATELY 4.9.
NEXT QUESTION IS THE PH OF VINEGAR IS 3.
WHAT IS THE HYDROGEN ION CONCENTRATION?
SO NOW THEY'RE GIVING US THE PH.
WE WANT TO SOLVE THE EQUATION FOR THE CONCENTRATION
OF HYDROGEN IONS.
SO WE WANT TO SOLVE THE EQUATION
3 EQUALS NEGATIVE COMMON LOG OF THE HYDROGEN ION CONCENTRATION.
NOW WE WANT TO ISOLATE THE LOGARITHM
SO WE'LL DIVIDE BOTH SIDES BY -1.
THIS IS JUST GOING TO CHANGE THE SIGN
ON BOTH SIDES OF THE EQUATION
SO NOW WE'LL HAVE -3 EQUALS
THE COMMON LOG OF THE HYDROGEN ION CONCENTRATION
AND FROM HERE WE NEED TO REMEMBER THAT THE COMMON LOG
IS LOG BASE 10.
SO NOW TO SOLVE THIS LOG EQUATION
WE'LL WRITE THIS AS AN EXPONENTIAL EQUATION.
REMEMBER 10 WOULD BE THE BASE, -3 WOULD BE THE EXPONENT
AND THE NUMBER WOULD BE THE HYDROGEN ION CONCENTRATION.
SO 10 TO THE -3 IS EQUAL TO THE HYDROGEN ION CONCENTRATION.
WELL, 10 TO THE -3 CAN BE WRITTEN AS
1 OVER 10 TO THE POSITIVE 3 POWER
WHICH IS EQUAL TO 1 OVER 1,000
OR IN DECIMAL FORM 1/1000TH WOULD BE 0.001.
THEREFORE THE HYDROGEN ION CONCENTRATION FOR THIS VINEGAR
WOULD BE 0.001 MOLES PER LITER
WHICH WE COULD EXPRESS WITH A CAPITAL M.
OKAY, THAT'S GOING TO DO IT FOR THIS EXAMPLE.
I HOPE YOU FOUND THAT HELPFUL.