SOLUTION: use properties of logarithms to find the exact value of each expression. log[base 3]8 * log[base8]9

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: use properties of logarithms to find the exact value of each expression. log[base 3]8 * log[base8]9      Log On


   

Question 415794: use properties of logarithms to find the exact value of each expression.
log[base 3]8 * log[base8]9
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
use properties of logarithms to find the exact value of each expression without using calculators.
log[base 3]8 * log[base8]9
..
Using change of base formula,
log8/log3*log9/log8
=log 2^3/log3*log3^2/log 2^3
cancel out log 2^3
=2log3/log3=2
ans:
log[base 3]8 * log[base8]9=2