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

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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

russelllomando

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

panlomito

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)

Stylux-zp

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

ARIGROSSMAN

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

stevendebettencourt

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

chrisdissanayake

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

argonwheatbelly

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

tomtke

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

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

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