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2021-07-11 18:40:34 +0100 commented answer Solve cannot get algebraic answer without taking logarithm

Thank you for the lucid detailed response to my issue. I feel fortunate to have stumbled into this problem rather than i

2021-07-11 18:37:41 +0100 marked best answer Solve cannot get algebraic answer without taking logarithm

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

I am new to Sage, so I assume that I am doing something wrong. I like the Jupyter notebook interface and am hoping to use 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 9.2

Fails:

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

Works:

sage: x = var('x')
sage: assume(x,'real')
sage: solve( ln(8^(3*x))-ln(16^(x+1))==0, x)
[x == (4/5)]
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2021-07-09 16:27:59 +0100 edited question Solve cannot get algebraic answer without taking logarithm

Solve cannot get algebraic answer without taking logarithm I'm trying to solve the simple, one variable equation: 8^(3*x

2021-07-08 19:29:27 +0100 asked a question Solve cannot get algebraic answer without taking logarithm

Solve cannot get algebraic answer without taking logarithm sagemath 9.2 Fails: x = var('x') assume(x,'real') solve( 8^