Solve 8 to the x = 16 to the 4x -1 with no calculator - Algebra Exponential Equations

[@Stylux-z1p]

2³ = 8 and 2^4 = 16 8^x = 16^4x-1 (2³)^x = (2^4)^4x - 1 (2)^3x = (2)^4(4x - 1) -> Regels van machten:(a²)³ = (a)² * ³ = a^6 3x = 4(4x - 1) ---> Exponentiation Rule of Equality if a^n = a^m --> m = n 3x = 16x - 4 --> distributieve eigenschap van vermenigvuldiging 4 = 16x - 3x --> gelijksoortige termen aftrekken 4 = 13x 4/13 = 13x / 13 4/13 = x ✅ proef op de som : 8^x = 16^4x-1 8^(4/13) = 16^(4 * (4 / 13) - 1) 8^(4/13) = 16^(16/ 13) - 1) (2³)^(4/13) = (2^4)^(16/ 13) - 1) (2)³ * (4/13) = (2)^4((16/13) - 1) (2)^(12/13) = (2)^((64/13) - 4) (2)^(12/13) = (2)^((4 +12/13) - 4) (2)^(12/13) = (2)^(12/13)

[@panlomito]

2^(3x) = 2^4.(4x-1) = 2^(16x-4) so 3x = 16x - 4 -> 13.x = 4 and x = 4/13

[@chrisdissanayake6979]

8^x = 16^4x-1 (2^3)^x = (2^4)^4x-1 2^3x = 2^16x-4 3X= 16x-4 3x-16x = -4 -13x = -4 13x = 4 x = 4/13

[@stevendebettencourt7651]

Knowledge of what you can do with exponents and logarithms is vital to this one. I got x=4/13.

[@ARIGROSSMAN]

Step by step you are simple and precise. I sure wish I had you as my calculusc2vteacher.

[@russelllomando8460]

got 4/13 converted 8 to 2^3 and 16 to 2^4 then multiplied exponents to 3X and 16X-4 they are = as are the bases of 2. 3X=16X-4 and solve easy thanks for the fun

[@argonwheatbelly637]

x=4/13 in about 10 seconds in my head. Took way too long, but this was a fun one!

[@bazkeen]

Nice one 👍🏻

[@tomtke7351]

8^x=16^(4x-1) xlog8=(4x-1)log16 4x-1=x(log8/log16) 4x-1=x(0.75) 4x-0.75x=1 3.25x=1 x=1/3.25 =0.3077 VERIFY x=0.3077 8^x=16^(4x-1) 8^0.3077=?16^((4×0.3077)-1) 1.8962=?16^(0.2308) 1.8962=❤1.8963✔️ oops... no calculator

[@mikiokabe6689]

Easy❤ 4/13

[@josephlaura7387]

x= 4/13

[@jiyoungpark6233]

x=2...

[@jiyoungpark6233]

x=1/4...

[@FlugHerr]

X= 4/13