Conversion of bases with logarithms The question says if log_6(2) is a and log_5(3) is b, express

Alexandra Richardson 2022-07-23 Answered
Conversion of bases with logarithms
The question says if log 6 ( 2 ) is a and log 5 ( 3 ) is b, express log 5 ( 2 ) in terms of a and b
I have tried the change of base formula for a b to no avail, can someone give me a hint to get started, and the solution, hidden behind a spoiler tag, if I get stuck? Thanks.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

autosmut6p
Answered 2022-07-24 Author has 8 answers
Write down the expressions for a and b and define your target as c:
a = log 6 ( 2 ) = ln ( 2 ) ln ( 6 )
b = log 5 ( 3 ) = ln ( 3 ) ln ( 5 )
c = log 5 ( 2 ) = ln ( 2 ) ln ( 5 )
Now use ln ( 6 ) = ln ( 2 ) + ln ( 3 ) and get
c = ln ( 2 ) ln ( 5 ) = ln ( 2 ) ln ( 6 ) ln ( 6 ) ln ( 5 ) = ln ( 2 ) ln ( 6 ) ln ( 2 ) + ln ( 3 ) ln ( 5 )
c = ln ( 2 ) ln ( 6 ) ln ( 2 ) ln ( 5 ) + ln ( 2 ) ln ( 6 ) ln ( 3 ) ln ( 5 ) = a c + a b
Now solve for c and get the solution
c = a b 1 a
And to be sure you can do a sanity check
a = log 6 ( 2 ) 0.386853
b = log 5 ( 3 ) 0.682606
c = log 5 ( 2 ) 0.430677
a b 1 a 0.386853 × 0.682606 1 0.386853 0.430676785 c
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more