Mathematica can't simplify some logarithmic expressions

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When I simplify some logarithmic expressions in Mathematica, it just returns the expression

FullSimplify[Log[Sqrt[2] + 1, 5 Sqrt[2] + 7]]

FullSimplify[Log[Sqrt[2] + 1, 17 - 12 Sqrt[2]]]

enter image description here

Obviously, simplification isn't completely, using Maple could get
enter image description here

Is there any way I can tell Mathematica to be smarter?

edited 1 hour ago

asked 2 hours ago

mathe

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up vote
2
down vote

favorite

When I simplify some logarithmic expressions in Mathematica, it just returns the expression

FullSimplify[Log[Sqrt[2] + 1, 5 Sqrt[2] + 7]]

FullSimplify[Log[Sqrt[2] + 1, 17 - 12 Sqrt[2]]]

enter image description here

Obviously, simplification isn't completely, using Maple could get
enter image description here

Is there any way I can tell Mathematica to be smarter?

edited 1 hour ago

asked 2 hours ago

mathe

2,46611642

add a commentÂ |Â

up vote
2
down vote

favorite

When I simplify some logarithmic expressions in Mathematica, it just returns the expression

FullSimplify[Log[Sqrt[2] + 1, 5 Sqrt[2] + 7]]

FullSimplify[Log[Sqrt[2] + 1, 17 - 12 Sqrt[2]]]

enter image description here

Obviously, simplification isn't completely, using Maple could get
enter image description here

Is there any way I can tell Mathematica to be smarter?

edited 1 hour ago

asked 2 hours ago

mathe

2,46611642

When I simplify some logarithmic expressions in Mathematica, it just returns the expression

FullSimplify[Log[Sqrt[2] + 1, 5 Sqrt[2] + 7]]

FullSimplify[Log[Sqrt[2] + 1, 17 - 12 Sqrt[2]]]

enter image description here

Obviously, simplification isn't completely, using Maple could get
enter image description here

Is there any way I can tell Mathematica to be smarter?

simplifying-expressions algebraic-manipulation

edited 1 hour ago

asked 2 hours ago

mathe

2,46611642

edited 1 hour ago

asked 2 hours ago

mathe

2,46611642

edited 1 hour ago

asked 2 hours ago

mathe

2,46611642

asked 2 hours ago

mathe

2,46611642

asked 2 hours ago

mathe

2,46611642

add a commentÂ |Â

1 Answer
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4
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Use RootApproximant

y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

y1 // RootApproximant

(* 3 *)

Verifying,

y1 == 3 // FullSimplify

(* True *)

y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

y2 // RootApproximant

(* -2 *)

Verifying,

y2 == -2 // FullSimplify

(* True *)

answered 1 hour ago

Bob Hanlon

56.5k23591

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1 Answer
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active

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1 Answer
1

active

oldest

votes

up vote
4
down vote

Use RootApproximant

y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

y1 // RootApproximant

(* 3 *)

Verifying,

y1 == 3 // FullSimplify

(* True *)

y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

y2 // RootApproximant

(* -2 *)

Verifying,

y2 == -2 // FullSimplify

(* True *)

answered 1 hour ago

Bob Hanlon

56.5k23591

add a commentÂ |Â

up vote
4
down vote

Use RootApproximant

y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

y1 // RootApproximant

(* 3 *)

Verifying,

y1 == 3 // FullSimplify

(* True *)

y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

y2 // RootApproximant

(* -2 *)

Verifying,

y2 == -2 // FullSimplify

(* True *)

answered 1 hour ago

Bob Hanlon

56.5k23591

add a commentÂ |Â

up vote
4
down vote

Use RootApproximant

y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

y1 // RootApproximant

(* 3 *)

Verifying,

y1 == 3 // FullSimplify

(* True *)

y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

y2 // RootApproximant

(* -2 *)

Verifying,

y2 == -2 // FullSimplify

(* True *)

answered 1 hour ago

Bob Hanlon

56.5k23591

Use RootApproximant

y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

y1 // RootApproximant

(* 3 *)

Verifying,

y1 == 3 // FullSimplify

(* True *)

y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

y2 // RootApproximant

(* -2 *)

Verifying,

y2 == -2 // FullSimplify

(* True *)

answered 1 hour ago

Bob Hanlon

56.5k23591

answered 1 hour ago

Bob Hanlon

56.5k23591

answered 1 hour ago

Bob Hanlon

56.5k23591

answered 1 hour ago

Bob Hanlon

56.5k23591

add a commentÂ |Â

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