SOLUTION: Find the value of the expression log8 32 Ans:5/3

Question 277821: Find the value of the expression
log8 32

Ans:5/3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

As it is, this logarithm cannot be found. No calculator "knows" base 8 logarithms and 32 is not a known power of 8. So what we need to do is transform this logarithm into an expression we can find. Fortunately there is a base conversion formula, , which we can use to change this base 8 logarithm into a logarithm we can find.

So we need to choose a base to change the base 8 logarithm into. I'll choose two different bases.
Base 2. Since 8 is a power of 2 (), using base 2 has some promise of making the problem easier. Using the conversion formula to convert the base 8 logarithm into an expression of base 2 logarithms we get:

As stated earlier 8 is 2 cubed. So the logarithm in the denominator is 3. And, as it turns out 32 is also a power of 2! . So the logarithm in the numerator is 5. This makes our expression:
5/3
And we are finished (except perhaps changing the improper fraction into a mixed number).

If 8 had not been a power of 2 or if we didn't recognize that 8 (or 32) was a power of 2, then we would need to cahnge the base to one our calculator "knows" (like base 10 or base e (ln)). Converting your expression into base 10 logarithms we get:

And now we would use our calculators to find the two logarithms and them divide. The first way is better than this way. For one, calculators use decimal approximations for most logarithms. Secondly, the decimal answer you get from a calculator may by hard to recognize as equal to the fraction 5/3.
RELATED QUESTIONS
If log8 3 = 0.5283 and log8 5 = 0.7740, then what is the value of log8 45... (answered by nerdybill)

find the value of log8... (answered by lwsshak3)

find the value of... (answered by lwsshak3)

Find the value of log8... (answered by MathLover1)

use the properties of logarithms and the values below to find the logarithm indicated. (answered by ankor@dixie-net.com)

Given that log8 5 = 0.7740 and log8 11 = 1.1531 evaluate the expression log8... (answered by Alan3354)

Given that log8 5 = 0.7740 and log8 11 = 1.1531 evaluate the expression log8... (answered by Boreal,ikleyn)

what is the value of log8... (answered by Edwin McCravy)

what is the value of log8... (answered by lwsshak3)