MaxWong

Not correct......

Ans: \(x = \sqrt[n]{n}\)

The dots mean the "x"s goes infinitely...... That means left hand side is "x to the power x to the power x to the power x to the power x........ going infinitely".......

UHHHHHHHHHHHHH LOL

No need to be a Maths question every time..... :)

Am I the first one to discover this solution?

(Edited on 5 May 2022: Probably not, this is basic calculus.)

ABCDE = 42857.

This is a really common question in Hong Kong's Maths competition and I have to remember this special number so that once I see the question I know it is related to 142857.

\(\dfrac{\left(3x^2y^3\right)\left(2xy^2\right)^2}{-2x^2y}\\ =\dfrac{\left(3\cdot 2\right)\cdot\left(x^2\cdot x^2\right)\cdot\left(y^3\cdot y^4\right)}{-2x^2y}\\ =\dfrac{6x^4y^7}{-2x^2y}\\ =\left(\dfrac{6}{-2}\right)\left(\dfrac{x^4}{x^2}\right)\left(\dfrac{y^7}{y}\right)\\ =-3x^2y^6\)

~The smartest cookie in the world.

To asinus:

The 6th step:

\(\lg x^{10} = 15 - \lg 273375\\ 10 \lg x = 15 - \lg 273375\\ x = 10^{\frac{15-\lg 277375}{10}}\)

Because the right hand side is already a numerical value and the left hand side is x, so this can be the solution. 

No need to do all that..... LOL 

~The smartest cookie in the world

\(\quad h\\ = \dfrac{18\tan 9 \tan 3.5}{\tan 9}-\tan 3.5\\ =18\tan 3.5 - \tan 3.5\\ = 17\tan 3.5\)

\(1\dfrac{1}{4}\cdot 1 \cdot \dfrac{1}{4}\\ = \dfrac{5}{4}\cdot \dfrac{1}{4}\\ = \dfrac{5}{16}\)

\(\displaystyle\lim_{\theta\rightarrow 0}\dfrac{\sin5\theta}{\theta}\\ =\displaystyle\lim_{\theta\rightarrow 0}5\cdot \dfrac{\sin 5\theta}{5\theta}\\ = 5\cdot \displaystyle\lim_{\theta\rightarrow 0} \dfrac{\sin 5\theta}{5\theta}\\ =5\cdot 1\\ = 5 \\ \boxed{\cdot\;\cdot\\ \smile}\)

This is just the visualization of CPhill's answer......