completely forgot how to do this!! | Mathematics | Page 1

onyx wadi Jun 24, 2023, 10:30 PM

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pls help

fleet matrix Jun 24, 2023, 10:31 PM

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use the fact that 36 = 6^2

onyx wadi Jun 24, 2023, 10:31 PM

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yeah got that part

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but idk what to do after

fleet matrix Jun 24, 2023, 10:43 PM

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Do you know logarithms

stark sage Jun 24, 2023, 10:43 PM

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bascially

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if you rewrite 36 as 6^2

onyx wadi Jun 24, 2023, 10:44 PM

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fleet matrix Do you know logarithms

yes

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oh is it just ln on both sides

stark sage Jun 24, 2023, 10:44 PM

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you get (6^2)^6x-3

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if u have a power to a power you multiply

fleet matrix Jun 24, 2023, 10:45 PM

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Take log base 6 of both sides

stark sage Jun 24, 2023, 10:45 PM

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and you get 6^3x=6^12x-6

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equate 3x and 12x-6

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9x=6

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x=6/9

fleet matrix Jun 24, 2023, 10:46 PM

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stark sage equate 3x and 12x-6

Nothing says equal

stark sage Jun 24, 2023, 10:46 PM

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fleet matrix Nothing says equal

trust me here bud

fleet matrix Jun 24, 2023, 10:46 PM

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Look at answer choices

stark sage Jun 24, 2023, 10:46 PM

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you so right

fleet matrix Jun 24, 2023, 10:47 PM

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Let’s solve it another way for confirmation

stark sage Jun 24, 2023, 10:47 PM

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let me shut up

onyx wadi Jun 24, 2023, 10:47 PM

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fleet matrix Take log base 6 of both sides

wdym both sides?

fleet matrix Jun 24, 2023, 10:47 PM

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Because you have to do same thing on both sides

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To equate

onyx wadi Jun 24, 2023, 10:47 PM

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yeah

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are u using 6^3x=4?

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is that what ur doing log base 6 on?

fleet matrix Jun 24, 2023, 10:48 PM

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Yea

onyx wadi Jun 24, 2023, 10:48 PM

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ohhh i see

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would it be log6 (4)=3x?

fleet matrix Jun 24, 2023, 10:50 PM

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Yea

stark sage Jun 24, 2023, 10:50 PM

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is this a calculator question

onyx wadi Jun 24, 2023, 10:50 PM

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no calculator

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sorry should’ve said that

stark sage Jun 24, 2023, 10:50 PM

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ok ok

onyx wadi Jun 24, 2023, 10:50 PM

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fleet matrix Yea

what would i do after

fleet matrix Jun 24, 2023, 10:50 PM

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Rewrite log6 (4)

onyx wadi Jun 24, 2023, 10:51 PM

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wdym

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like expand it?

fleet matrix Jun 24, 2023, 10:52 PM

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Change of base

onyx wadi Jun 24, 2023, 10:52 PM

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or like log(4)/log(6)

fleet matrix Jun 24, 2023, 10:52 PM

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Yea

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Then divide both sides by 3

onyx wadi Jun 24, 2023, 10:52 PM

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okay

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x= 1/3(log(4)/log(6))

fleet matrix Jun 24, 2023, 10:53 PM

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Just rewrite the 3 in the denominator

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To make it easier

onyx wadi Jun 24, 2023, 10:53 PM

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okay

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3log6 in denominator

fleet matrix Jun 24, 2023, 10:53 PM

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Ok

onyx wadi Jun 24, 2023, 10:54 PM

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do i make that log(216) or no

fleet matrix Jun 24, 2023, 10:54 PM

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Now for the second you have 6^(12x-6)

fleet matrix Jun 24, 2023, 10:54 PM

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onyx wadi do i make that log(216) or no

no

onyx wadi Jun 24, 2023, 10:54 PM

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okay

onyx wadi Jun 24, 2023, 10:55 PM

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fleet matrix Now for the second you have 6^(12x-6)

yup

fleet matrix Jun 24, 2023, 10:55 PM

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We found x

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So multiply and simplify

onyx wadi Jun 24, 2023, 10:58 PM

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fleet matrix So multiply and simplify

we would get 6^(log(256)/log(6))-3

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how do u simplify that further

fleet matrix Jun 24, 2023, 11:02 PM

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Use the fact that 256 = 4^4 = 2^8

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Now we have to approximate

onyx wadi Jun 24, 2023, 11:03 PM

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approximate what

fleet matrix Jun 24, 2023, 11:04 PM

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10^x = 2

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So log 2 is about 0.3

onyx wadi Jun 24, 2023, 11:05 PM

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how’d u get that

fleet matrix Jun 24, 2023, 11:13 PM

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Actually

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I don’t know how to get an exact value

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But note that 6^3<256<6^4

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Thus that expression simplifies to around like 6^(3. some low number - 6)

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Then do 3-6

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And do 6^result

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But idk if your satisfied with that

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Sorry

zenith valve Jun 25, 2023, 8:00 AM

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onyx wadi pls help

You can solve it without log too though

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Now just substitute 4 at place of 6^3x

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And calculate answer

onyx wadi Jun 25, 2023, 7:27 PM

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thank you so much

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+close

#completely forgot how to do this!!