Properties of logarithmic functions

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
crescentcitycid
Posts: 5
Joined: Sun Feb 27, 2011 6:59 pm
Contact:

Properties of logarithmic functions

Postby crescentcitycid » Sun Feb 27, 2011 9:32 pm

I have a series of problems that state: given that logb(2)=.39, logb(3)=.61 and logb(5)=.9, find the following for logs, do no try to find "b"

Then there are easy ones to solve using multiplication and division properties, but there is one I'm not sure about.

blogb(5)

Can that go any further than b.9 ?

User avatar
stapel_eliz
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Postby stapel_eliz » Sun Feb 27, 2011 10:10 pm

crescentcitycid wrote:...there is one I'm not sure about.

blogb(5)

Can that go any further than b.9 ?

Yes. In fact, avoid that entirely. Instead of simplifying the exponent on , try setting up and solving an exponential equation:

. . . . .

...for some numerical value Then:

. . . . .

Apply a log rule to get:

. . . . .

Simplify the left-hand side, and the answer should pop out at you. :wink:

crescentcitycid
Posts: 5
Joined: Sun Feb 27, 2011 6:59 pm
Contact:

Re: Properties of logarithmic functions

Postby crescentcitycid » Sun Feb 27, 2011 10:18 pm

.9
Awesome, thank you.

User avatar
stapel_eliz
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Postby stapel_eliz » Sun Feb 27, 2011 10:37 pm

crescentcitycid wrote:.9

No. Try simplifying the left-hand side. Then look at what you have left.

crescentcitycid
Posts: 5
Joined: Sun Feb 27, 2011 6:59 pm
Contact:

Re: Properties of logarithmic functions

Postby crescentcitycid » Sun Feb 27, 2011 10:51 pm

Well if logb(5)=.9 and logbb=1 then .9(1)=.9

User avatar
stapel_eliz
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

Postby stapel_eliz » Mon Feb 28, 2011 12:48 am

Start with the equation I gave you earlier. Follow the instructions.

What is the expression for the right-hand side? What is the simplified (not "evaluated") form of the left-hand side?


Return to “Advanced Algebra ("pre-calculus")”