QUESTIONS - ANGELA - LOGARITHMS

QUESTIONS - ANSWERS -ANGELA - LOGARITHMS

Angela has left a new comment on your post "QUESTIONS - POLYNOMIALS":

1) Determine the value of the following function if a = 10 and x = 100, and tell which number is the base. log a^x 2) Determine the value of the following function if a = 2 and x = 1024. log a^x 3) Express log 2 10y as the sum or difference of two logarithms. 4) The definition of a google is the number 10^100. What is the base 10 logarithm of a google? Thank you!

AS YOU KNOW IF
B^P = N …WE SAY THAT
LOGARITHM OF ‘N’ WITH RESPECT TO BASE ‘B’ IS ‘P’.
GENERALLY WE ADOPT TWO BASE VALUES TO TABULATE LOGARITHMS.THEY ARE BASE 10 AND BASE ‘E’….AN IRRATIONAL NUMBER OFTEN ENCOUNTERED IN MATHEMATICS.
THE NORMAL CONVENTION IS TO USE
LOG(X)..TO INDICATE LOGARITHMS TO BASE 10 .....
LN(X) ..TO INDICATE LOGARITHMS TO BASE ‘E’. AND
IF ANY OTHER BASE IS ADOPTED,THEN TO SPECIFY IT AS A SUFFIX AFTER LOG TO BE FOLLOWED BY THE NUMBER LATER.THAT IS WE HAVE TO WRITE LOG TO BASE B OF N.

NOW ON TO YOUR PROBLEMS.HAVE YOU TYPED THEM PROPERLY.I THINK YOU MAY BE MEANING
LOG(X) TO BASE ‘A’[‘A’ IS PUT AS A SUFFIX AFTER LOG THEN FOLLOWED BY X].ANY WAY FOR THE FIRST QUESTION ,I AM GIVING ANSWERS TO 2 VARIANTS…AS YOU TYPED AND AS I THINK IT MAY BE.FOR THE OTHER PROBLEMS , I AM GIVING THE ANSWER ASSUMING MY INTERPRETATION OF YOUR TYPING.

1.AS YOU TYPED.
HENCE GOING BY THIS CONVENTION WE GET..
LOG(A^X)=X*LOG(A)=100LOG(10)=100*1=100
SINCE LOG(10) IS UNDERSTOOD TO BE TO BASE 10
BY THE ABOVE NOMENCLATURE AND AS WE KNOW
10^1 =10 AND HENCE LOG(10) TO BASE 10 =1

AS PER MY INTERPRETATION OF YOUR TYPING
1. LOG(100) TO BASE 10 =2…SINCE
10^2 =100
2. LOG (1024) TO BASE 2 = 10……SINCE
2^10 = 1024
3. LOG (10Y) TO BASE 2 = LOG(10) TO BASE 2 + LOG(Y) TO BASE 2.