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Mathematics 46 Online
OpenStudy (anonymous):

1/4 log 2 16 + 1/2 log 2 49 = log 2 x What is the solution to this?

OpenStudy (anonymous):

Please help!

OpenStudy (ash2326):

@KayJanae I'll help you. Do you know the basic properties of logarithms?

OpenStudy (anonymous):

No I dont

OpenStudy (ash2326):

okay, the following are important \[1)\log_x y=z \longrightarrow y=x^z\] \[2) a\log b=\log b^a\] \[3) \log x+\log y=\log xy\] \[4) \log x-\log y=\log\frac xy\]

OpenStudy (anonymous):

Alright, and do they have a certain name?

OpenStudy (anonymous):

Ignore that question lol where do we go from here?

OpenStudy (ash2326):

Yeah, let me pull a website, where will you get the names also

OpenStudy (anonymous):

Ok, thanks

OpenStudy (ash2326):

do check this http://en.wikipedia.org/wiki/Logarithm let's work on the problem

OpenStudy (anonymous):

ok

OpenStudy (ash2326):

We have \[\frac 14 \log_2 16 +\frac 1 2 \log_2 49 = \log_2 x\] one more thing, all those properties only if the base is same

OpenStudy (anonymous):

Ok, the base is 2 right?

OpenStudy (ash2326):

yeah, here all have same, so we could use the properties tell me what's this ? \[\frac 14 \log_2 16\] use one of the properties to simplify

OpenStudy (anonymous):

Um, how do i do that?

OpenStudy (anonymous):

\[16^{1/4} * 49^{1/2} =x\]

OpenStudy (anonymous):

That isnt right. It isnt one of the choices

OpenStudy (anonymous):

\[16^{1/4} * 49^{1/2} = 2*7 =14\]

OpenStudy (anonymous):

Ohh ok thank you, could you do another one for me?

OpenStudy (anonymous):

log 3 0.1 + 2log 3 x = log 3 2 + log 3 5

OpenStudy (anonymous):

The principle is the same, just as ash2326 showed you: \[0.1 * x ^{2} = 2 * 5\] that's what your above expression reduces to, remember when you add logs, you multiply the real numbers, and when you subtract logs, you divide the real numbers. can you try solve this one

OpenStudy (anonymous):

\[0.1x ^{2} = 10\] \[x ^{2} = 10/0.1 = 100\] \[x=10\]

OpenStudy (anonymous):

ok.. i think i understand, so the answer to my question is 10?

OpenStudy (anonymous):

yh

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