Properties of logarithmic functions

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
crescentcitycid
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Properties of logarithmic functions

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 ?

stapel_eliz
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...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 $b$, try setting up and solving an exponential equation:

. . . . .$b^{\log_b(5)}\, =\, x$

...for some numerical value $x.$ Then:

. . . . .$\log_b\left(b^{\log_b(5)}\right)\, =\, \log_b(x)$

Apply a log rule to get:

. . . . .$\log_b(5) \times \log_b(b)\, =\,...?$

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

crescentcitycid
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Re: Properties of logarithmic functions

.9
Awesome, thank you.

stapel_eliz
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.9
No. Try simplifying the left-hand side. Then look at what you have left.

crescentcitycid
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Re: Properties of logarithmic functions

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

stapel_eliz
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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?