how do you do this with no calculator | Mathematics | Page 1

wraith stag Feb 1, 2026, 9:04 AM

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help me 🥲🥲

harsh cradleBOT Feb 1, 2026, 9:04 AM

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real geyser Feb 1, 2026, 9:10 AM

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wraith stag help me 🥲🥲

You first use the rule log a^b = b loga

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Omg i cant be bothered typing this

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Lets just say log_2026 = z

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It wiuld be z15 zx + z3 zx = 1012

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And u split into bracket

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Log_2026 x( z3 + z15) = 1012

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Use the formula log a + log b = logab

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Log_2026 x ( log_2026 45) = 1012

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U turn 1012 into terms of log_2026

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Which is just z 2026^1012

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Hmm

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You kinda need a calc for this

wraith stag Feb 1, 2026, 9:24 AM

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I might actually

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gonna skip this question ✌️ ✌️

real geyser Feb 1, 2026, 9:24 AM

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Wait

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45^2 =2,025

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Which is close to 2026

wraith stag Feb 1, 2026, 9:26 AM

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45^1012

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? 😭 😭

real geyser Feb 1, 2026, 9:27 AM

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?

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U should get

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Log_2026 45 times log_2026 x = 1012

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Log 2026_x = 1012/log_2026 x

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X = 2026^(fraction)

topaz steeple Feb 1, 2026, 9:31 AM

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you could probably do a substitution to cancel out the annoying logs

real geyser Feb 1, 2026, 9:31 AM

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No wait

topaz steeple Feb 1, 2026, 9:31 AM

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mayhaps x = 2026^a

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then deal with that later

real geyser Feb 1, 2026, 9:31 AM

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Log 2026 45 is really close to log 2025 45

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U can approximate it to 2

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I mean

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1/2

topaz steeple Feb 1, 2026, 9:32 AM

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topaz steeple mayhaps x = 2026^a

yeah this is easier

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this should cancel a lot of stuff out

real geyser Feb 1, 2026, 9:32 AM

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1/loga b = logb a

real geyser Feb 1, 2026, 9:32 AM

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topaz steeple yeah this is easier

Yeah ig😭

topaz steeple Feb 1, 2026, 9:33 AM

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though i doubt you will get the nice result and you need to use change of base

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but that's about it

real geyser Feb 1, 2026, 9:33 AM

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Youd still have to estimate

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1012/log_2026 45 = 1012/log_45 2026

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Log_45 2025 = 2

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So you can estimate log_45 2026 to around 2

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X =2026^1012x2 = 2026^2024

winged frigate Feb 1, 2026, 9:35 AM

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real geyser X = 2026^(fraction)

,, x=2026^{\frac{1012}{\log _{2026}45}}

jolly muskBOT Feb 1, 2026, 9:35 AM

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firestepper

winged frigate Feb 1, 2026, 9:36 AM

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,w log (45)/log(2026)

real geyser Feb 1, 2026, 9:36 AM

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I dont think theres way to do without estimate?

jolly muskBOT Feb 1, 2026, 9:36 AM

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winged frigate Feb 1, 2026, 9:37 AM

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yh 0.5

real geyser Feb 1, 2026, 9:37 AM

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Without calculator😭

winged frigate Feb 1, 2026, 9:37 AM

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oh hm..

real geyser Feb 1, 2026, 9:38 AM

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I mean u just gotta hope youve memorized the power table

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45^2 =2,025

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Or find it someway

winged frigate Feb 1, 2026, 9:40 AM

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hm.. i dont think you might find a nice trick

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approximation it is

winged frigate Feb 1, 2026, 9:41 AM

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jolly musk **firestepper**

this is exponential form tho they should accept this

real geyser Feb 1, 2026, 9:41 AM

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winged frigate this is exponential form tho they should accept this

Accepted answers are below😭

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But i mean in an exam they might accept it

winged frigate Feb 1, 2026, 9:42 AM

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🤷‍♂️ is on professor

wraith stag Feb 1, 2026, 9:43 AM

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thank u thank u 🙏🙏🙏

wraith stag Feb 1, 2026, 10:21 AM

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I get it now

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💃

real geyser Feb 1, 2026, 10:23 AM

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🔥🔥

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U might want to show that u estimated to get 1/2

wraith stag Feb 1, 2026, 10:24 AM

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right right thanks 🫶🫶

tranquil thistle Feb 1, 2026, 3:42 PM

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I feel like the answer is kind of weird ngl since log_2026(45) is not 1/2

wraith stag Feb 2, 2026, 4:53 AM

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tranquil thistle I feel like the answer is kind of weird ngl since log_2026(45) is not 1/2

the question was also wrong I think 😭😭😭

real geyser Feb 2, 2026, 5:08 AM

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tranquil thistle I feel like the answer is kind of weird ngl since log_2026(45) is not 1/2

nah the difference between log 2026 and log 2025 is insignificant

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so we can ignore it and just write 0.5

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and besides most curriculums require rounding

#how do you do this with no calculator