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sagemath 9.2

Fails: x = var('x') assume(x,'real') solve( 8^(3x)-16^(x+1)==0, x) output: [8^x == 1/216^(1/3x + 1/3)(Isqrt(3) - 1), 8^x == -1/216^(1/3x + 1/3)(Isqrt(3) + 1), 8^x == 16^(1/3x + 1/3)]

Works: x = var('x') assume(x,'real') solve( ln(8^(3*x))-ln(16^(x+1))==0, x) output: [x == (4/5)]

sagemath 9.2

Fails: x = var('x') assume(x,'real') solve( 8^(3x)-16^(x+1)==0, x) output: [8^x == 1/216^(1/3x + 1/3)(Isqrt(3) - 1), 8^x == -1/216^(1/3x + 1/3)(Isqrt(3) + 1), 8^x == 16^(1/3x + 1/3)]

Works: x = var('x') assume(x,'real') solve( ln(8^(3*x))-ln(16^(x+1))==0, x) output: [x == (4/5)]

I'm trying to solve the simple, one variable equation: 8^(3*x) = 16^(x+1).

I am new to sage, Sage, so I assume that I am doing something wrong. I like the Jupyter notebook interface and am hoping to use sagemath SageMath as my "go to" tool.

Mathematica, wolframalpha, and Mathcad 6 (mupad symbolic engine) solve this as is (x=4/5).

Sage and Mathcad 7 (new symbolic engine) both seem to require what would be the first step if I were to do manual solve -- take log of both sides.

sagemath SageMath 9.2

Fails: Fails:

sage: x = var('x')
sage: assume(x,'real')
sage: solve( 8^(3x)-16^(x+1)==0, 8^(3*x)-16^(x+1)==0, x)
output: [8^x == 1/216^(1/3x 1/2*16^(1/3*x + 1/3)(Isqrt(3) 1/3)*(I*sqrt(3) - 1), 1),
 8^x == -1/216^(1/3x -1/2*16^(1/3*x + 1/3)(Isqrt(3) 1/3)*(I*sqrt(3) + 1), 1),
 8^x == 16^(1/3x 16^(1/3*x + 1/3)]1/3)]

sage: x = var('x')
sage: assume(x,'real')
sage: solve( ln(8^(3*x))-ln(16^(x+1))==0, x)
output: [x == (4/5)]
(4/5)]