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Find the value of x?
How to solve 4^x+1 - 4^x-1 = 5

In this video, we'll show you How to Solve Math Olympiad Question A Nice Exponential Equation 4^x+1 - 4^x-1 = 5 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #maths #math #algebra

[subratabiswas]

4.4^x-4^x/4=5 ; i, e 16.4^x-4^x=20 ; i, e 15.4^x= 20; i, e 4^x= 4/3 ; i, e x= log(4/3)/log4 ; i, e x=( log4-log3)/log4 ; i, e x=1-(log3/2log2)

[nasrullahhusnan]

[4^(x+1)]-[4^(x-1)]=5
4(4^x)-¼(4^x)=5
(4-¼)(4^x)=5 --> 4^x=5/(4-¼)
=20/15
4^(x-1)=⅓
Take logarithm
(x-1)log(4)=log(⅓)
x=1-[log(3)]/log(4)

[rabotaakk-nwnm]

(4^x)4-(4^x)/4=5; 16(4^x)-4^x=20
15(4^x)=20; 4^x=20/15=4/3………
x=1-log(4)3=1-ln3/ln4≈0.2075 😁

[quinty.support]

4^(x+1) - 4^(x-1) = 5
4^(x) • 4^(1) - 4^(x) • 4^(-1) = 5
=> 4^(x) [4^(1) - 4^(-1)] = 5
=> 4^(x) [4-1/4] = 5
=> 4^(x) • 15/4 = 5
=> 4^(x) = (5•4)/15 = 20/15 = 4/3

ln(4^(x)) = ln(4/3)
=> xLn(4) = Ln(4/3)
=> x = Ln(4/3)/Ln(4)
=> x = [Ln(4) - Ln(3)]/Ln(4)
=> x = {2•Ln(2)-Ln(3)}/2•Ln(2)

[key_board_x]

4^(x + 1) - 4^(x - 1) = 5
[4^(x) * 4^(1)] - [4^(x) * 4^(- 1)] = 5
[4^(x) * 4] - [4^(x) / 4^(1)] = 5
[4^(x) * 4] - [4^(x) / 4] = 5 → by multiplying by 4 both sides
[4^(x) * 16] - 4^(x) = 20
15 * 4^(x) = 20
4^(x) = 20/15
4^(x) = 4/3
Ln[4^(x)] = Ln(4/3)
x.Ln(4) = Ln(4/3)
x = Ln(4/3) / Ln(4) → to go further
x = [Ln(4) - Ln(3)] / Ln(4)
x = [Ln(2²) - Ln(3)] / Ln(2²)
x = [2.Ln(2) - Ln(3)] / 2.Ln(2)

[quynhnguyen]

ANH 42 TUỔI RỒI. KHÔNG TRẺ NỮA. HAM HỌC HỎI VÀ YÊU AGENTINA.