A Nice Algebra Problem | Math Olympiad | Find the value of x?

[@fatihgaming9017]

Solusi termudah pd kasus ini adl dg mencoba beberapa angka. Angka 2 tembakan yg dpt langsung diprediksi. Ternyata benar.
Carilah solusi termudah dlm memecahkan masalah.!
Cara memprediksi jawaban adl ilmu yg perlu dipelajari juga..

[@SALogics]

Bagus sekali! ❤

[@justanotherdatanmfamily]

smart bro, 😎

[@SALogics]

Thanks! 😃

[@walterwen2975]

Math Olympiad: 6ˣ⁻¹ = x + 4; x =?
6(6ˣ⁻¹) = 6ˣ = 6(x + 4), 6ˣ = 6x + 24 > 0, x > - 4
x = 3, 6ˣ = 6³ = 216 > 6x + 24 = 6(3) + 24 = 42; 3 > x > - 4
6ˣ - 6x = 24 = 6(4) = 6(6 - 2) = 6² - 6(2); x = 2
Trial-and-error math to find the negative root;
6ˣ = 6(x + 4) = 6x + 24
x = - 3: 6ˣ⁻¹ = 1/6⁴ < 6(x + 4) = 6(- 3 + 4) = 6
x = - 4: 6⁻⁵ = 1/6⁵ > 6(- 4 + 4) = 0; - 3 > x > - 4, Slightly > - 4
x = - 3.99000; 6⁻⁴·⁹⁹⁰⁰⁰ = 0.0001309 < 4 - 3.99000 = 0.01000
x = - 3.99990; 6⁻⁴·⁹⁹⁹⁹⁰ = 0.0001286 > 4 - 3.99990 = 0.00010, Slightly > - 3.9999
x = - 3.99988; 6⁻⁴·⁹⁹⁹⁸⁸ = 0.0001286 ≈ 4 - 3.99988 = 0.00012
The calculation was achieved on a smartphone with a standard calculator app
Answer check:
x = 2 or x = - 3.99988: 6ˣ⁻¹ = x + 4; Confirmed as shown
Final answer:
x = 2 or x = - 3.99988

[@SALogics]

Very nice! ❤

[@LuzAydeChaverraTorres]

X=2

[@SALogics]

Very nice! ❤

[@zawatsky]

Совершенно непрозрачная функция, принцип действия которой нельзя точно описать простому обывателю. Которая просто "есть в калькуляторе и всё". Такие ответы - немного больше, чем никаких.

[@SALogics]

Very nice! ❤

[@pspprabhat]

6^×-1=x+4
=>1=(×+4).6^(-×+1)
=>{(-1)6^-4=(-6).6^-6
=W(-6.ln6)(e^ln6(-6)}=
W{(-×-4).e^ln6(-×+1-5)}....
.=>-6Ln6=(-×-4)ln6
=>-6+4=-×....=>×=2

[@SALogics]

Very nice! ❤