An Interesting Exponential Equation

[@KennethChile]

Thanks! I did the same, but then applied the quadratic formula to the equation x²-2x-log(2) = 0 x=1±√(1+log2) same values than x=1±√log20.

[@ochukoobrikogho5587]

Yes, I did. Thank you Sir

[@broytingaravsol]

x=1±√(1+log2)

[@goldfing5898]

10^(x^2) = 2 * 100^x Take the logarithm to base 10, which I call lg(), not log() !!! on both sides: lg(10^(x^2)) = lg(2 * 100^x) On the left side, we have just x^2, since lg(x) is the inverse function of 10^x. On the right side, we apply the logarithm rules: lg(2) + lg(100^x) = lg(2) + x * lg(100) = lg(2) + x * lg(10^2) = lg(2) + x * 2 Our equation now is as follows: x^2 = 2x + lg(2) x^2 - 2x - lg(2) = 0 which is a quadratic in x. Rather than using the quadratic formula, I add lg(2): x^2 - 2x = lg(2) and complete the square by adding 1: x^2 - 2x + 1 = 1 + lg(2) (x - 1)^2 = 1 + lg(2) = lg(10) + lg(2) = lg(10 * 2) = lg(20) x - 1 = +- sqrt(1 + lg(2)) x = 1 +- sqrt(1 + lg(2)) Since 1 + lg(2) = lg(10) + lg(2) = lg(10 * 2) = lg(20) you could also write x = 1 +- sqrt(lg(20)) The numerical values are x1 = +2.1406270186 x2 = -0.1406270186

[@robertlunderwood]

"log" is the appropriate mathematical notation, especially for base 10.

[@erikroberts8307]

Have you ever thought about doing a few problems in your series that relate to spherical trigonometry?

[@mehrdadbasiri9968]

Great as always it is...👍👍👍.

[@SyberMath]

❤️

[@adamrussell658]

I converted 2 to 10^log2 at the beginning but it comes out the same.

[@MathOrient]

It is indeed interesting :)

[@eckhardfriauf]

Gorgeous.

[@SyberMath]

Thank you! 😍

[@alextang4688]

It is obviously taking log for both sides and quadratic equation on x will be get. 👱‍♂👱‍♂👱‍♂👱‍♂👱‍♂👱‍♂

[@pedrovargas2181]

Vulgar log everything, then quadratic formula.

[@IorPerry]

am I the only that does not see the result of 10^(1+sqrt(log(20))^2 ?

[@onradioactivewaves]

It comes from taking the square root at almoat fonal step to get the 2 real solutions, one positive and one negative

[@IorPerry]

@@onradioactivewaves i mean, the numerical value is clipped in the video

[@onradioactivewaves]

@@IorPerry ya didnt see that