Solving a Log Equation with Different Bases

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Опубликовано:

27 июл 2024

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Комментарии : 77

@MrLidless Год назад

Convert the equation to natural logs: lnx / ln5 = 2ln5 / lnx (lnx)² = 2(ln5)² x = 5^±√2

@PinkPastelShark Год назад

When using change of base, you can save some steps by changing everything to log base 5 instead of a generic log so you can keep the LHS as one log

@Vash-hf2fb Год назад

I am not good at math, so I watch these videos to learn. Hopefully I get better.

@j.r.1210 Год назад

I think the simplest approach is to use the change of base formula, but applied only to the right-hand side of the equation. Just convert it to log[5]25/log[5]x. Then cross-multiplying, etc., leads straight to the answer.

@BurgoYT Год назад

Agree

@SyberMath Год назад

How?

@Rosee45 Год назад

Yeah... I Changed the base Easily i got the answer

@SuperYoonHo Год назад

Thank you!!!

@owlsmath Год назад

that was great! 😍 i think i did a 4th method but pretty close to method 1. Awesome video

@SyberMath Год назад

Awesome! Thank you!

@SuperYoonHo Год назад

Nice!

@jim2376 Год назад

I used change of base with 5 as the base. Led to the same result, 5^(+/-√2)

@lollmao9541 Год назад

Best way to do it Log 5 (x) = log x (25) Log 5 (x) = 2 log x (5) Log 5 (x) = 2 / log 5 (x) [(og 5 (x)]² = 2 Log 5 (x) = 2 X = 5^√2

@mathswan1607 Год назад

X=5^(sqrt(2)) or 5^(-sqrt(2))

@ytlongbeach 9 месяцев назад

i naturally went straight to the 2nd method. i'm a "change of base" kinda guy.

@damirdukic Год назад

As soon as I saw the problem, I immediately went with the 3rd method, since it's practically the most obvious one. The other two methods seem unnecessarily convoluted to me.

@tbg-brawlstars Год назад

x=5^(±√2) I did in mind in 10 seconds!!!

@SyberMath Год назад

Wow! 😁🤩

@tbg-brawlstars Год назад

@@SyberMath :D

@mdatik5517 Год назад

It's a very simple equation for solving in head.That: Logx/log5=log25/logx or,(logx)^2=2(log5)^2 or,logx=√2log5,-√2log5 or,x=5^√2,5^-√2 or,x=

@cesarrocha3647 Год назад

There is a small error at the 2nd method

@rakenzarnsworld2 Год назад

x = 5^(sqrt)

@kalimbesk4379 Год назад

hocam türkiyeden böyle bir içeriği ingilizce dilinde aktarmanıza bayıldım.. tebrik ederim

@SyberMath Год назад

Tesekkur ederim! 🥰

@kalimbesk4379 Год назад

@@SyberMath rica ederim hocam. Türkçe kanalınız varsa onu da takip etmek isterim

@Kire.riii. Год назад

I couldn't understand why 2log5's 2 become root 2 in next line's square...why not instead of 2???

@Phoenix-nh9kt Год назад

I solved it in my head in a few seconds

@davidseed2939 Год назад

me too, but i always forget the negative sqrt

@somebody.1026 Год назад

😂😂😂😂

@plamenpenchev262 Год назад

So did I but I missed x = 5^(-sqrt(2)). Logarithms are very important for Analytical Chemistry and I, as a chemist, must teach students because our mathematicians usually miss this material.

@rajatkumar1600 Год назад

Me too

@okohsamuel314 Год назад

@Phoenix ... But how do u prove that to people ... I mean we are not inside ur head🙄...so just how true is ur claim?🤔 ... 😂😂😂

@temujnbn9456 Год назад

I made up this equation but I don't know how to solve it Equation: logx(5x)=2x/5 Answer: 5

@user-em2hw6ng5i Год назад

Hello teacher 🙏

@SyberMath Год назад

Hello! 🤩

@stratosleounakis2267 Год назад

If we logarithmize whith a base of 5, a shorter solution is obtained. LOG X(5) = LOG 25(X) , LOG X(5) = LOG 25(5) / LOG X(5) LOG X(5) . LOG X(5) = 2 .....

@scottleung9587 Год назад

I used substitution.

@abioyebolanle7911 5 месяцев назад

Solve loga 27 + logb 4 = 5

@user-br2qp5fx3u 6 месяцев назад

I changed all baaes to base 5 and I got my answer write

@mehulpunia6174 Год назад

it's 5^√2

@giuseppemalaguti435 Год назад

X=5^(sqrt2),x=5^(-sqrt2)

@SyberMath Год назад

@vladimirkaplun5774 Год назад

Next video: can you solve x=1?

@SyberMath Год назад

Nope. Solve x-1=0 or x-1=x 😁😜

@vladimirkaplun5774 Год назад

@@SyberMath There are so many nice tasks and you are quite creative in them. Why do you select trivial ones?

@vladimirkaplun5774 Год назад

@@SyberMath For you from Sivashinsky text book x^4+(x+1)(5x^2-6x-6)=0 The author's solution is quite unobvious

@GirishManjunathMusic Год назад

Given: log_5 (x) = log_x (25) To find: x Using change-of-base: log(x)/log(5) = log(25)/log(x) As log(x) ≠ 0 by definition: (log(x))² = (log(25))·(log(5)) Using log(a²) = 2log(a): (log(x))² = 2·(log(5))·(log(5)) (log(x))² = 2·(log(5))² log(x) = ± √2·log(5) log(x) = log(5↑(±√2)) Taking both sides to the power of 10: x = 5↑(±√2)