SOLUTION: Approximate the logarithm using the properties of logarithms, given the values logb 2 ≈ 0.3562, logb 3 ≈ 0.5646, and logb 5 ≈ 0.8271. Round your result to four de

Algebra.Com
Question 678074: Approximate the logarithm using the properties of logarithms, given the values logb 2 ≈ 0.3562, logb 3 ≈ 0.5646, and logb 5 ≈ 0.8271. Round your result to four decimal places.
logb 32/125
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
The "trick" with these problems is to use properties of logarithms to rewrite the desired log in terms of the logs you've been given. So in this problem we will use properties to transform into an expression involving logs of 2, 3 and/or 5.

With a little effort we should be able to figure out that and . So can be written as:

Now we can start using properties to rewrite this in terms of logs of 2 and 5. First we use the property to split the numerator and denominator into separate logs:

Next we can use the property to move the exponents out of the arguments:

We now have expressed in terms of logs of 2 and 5. All we have to do now is substitute in the given values for these logs:

Simplifying...
RELATED QUESTIONS

Approximate the logarithm using the properties of logarithms, given the values logb(2)... (answered by ikleyn)
Approximate the logarithm using the properties of logarithms, given logb2=.3562,... (answered by stanbon,Theo,MathTherapy)
Approximate the following logarithm using the properties of logarithms given.... (answered by Alan3354)
Approximate the following logarithms using the properties of logarithms, given logb... (answered by josmiceli)
Approximate the logarithm using the properties of logarithms, given logb(2) ≈ 0.3562, (answered by greenestamps)
Given that logb(3)=0.16 and logb(5)=0.87 , use the properties of logarithms to find... (answered by josgarithmetic)
Use the properties of logarithms to rewrite each expression as a single logrythm. (logb... (answered by midwood_trail)
Can you please help to solve the following: Assume that log 4 ≈ 0.0602, log 5... (answered by stanbon,MathLover1)
Can you please help to solve the following: Assume that log 4 ≈ 0.0602, log 5... (answered by stanbon,richard1234)