# A Simple Exponential Equation

Sage can solve the equation $8^t =37$ for $t$:

```
solve( (8)^t ==37, t )
```

But strangely, cannot solve $\left(\frac 89\right)^t =37$

```
solve( (8/9)^t ==37, t )
```

Any ideas?

A Simple Exponential Equation

Sage can solve the equation $8^t =37$ for $t$:

```
solve( (8)^t ==37, t )
```

But strangely, cannot solve $\left(\frac 89\right)^t =37$

```
solve( (8/9)^t ==37, t )
```

Any ideas?

add a comment

0

Two workarounds :

```
sage: ((8/9)^t==37).log().log_expand().solve(t)
[t == -log(37)/(2*log(3) - 3*log(2))]
sage: solve((8/9)^t==37, t, algorithm="sympy")
[t == -log(37)/(2*log(3) - 3*log(2))]
```

Curiously :

```
sage: solve((8/9)^t==37, t, to_poly_solve="force")
[]
```

Worse :

```
sage: solve((8/9)^t==37,t, to_poly_solve=True)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-26-811d238787f4> in <module>
----> 1 solve((Integer(8)/Integer(9))**t==Integer(37),t, to_poly_solve=True)
/usr/local/sage-9/local/lib/python3.9/site-packages/sage/symbolic/relation.py in solve(f, *args, **kwds)
1041
1042 if is_Expression(f): # f is a single expression
-> 1043 return _solve_expression(f, x, explicit_solutions, multiplicities, to_poly_solve, solution_dict, algorithm, domain)
1044
1045 if not isinstance(f, (list, tuple)):
/usr/local/sage-9/local/lib/python3.9/site-packages/sage/symbolic/relation.py in _solve_expression(f, x, explicit_solutions, multiplicities, to_poly_solve, solution_dict, algorithm, domain)
1340 s = m.to_poly_solve(x, options='algexact:true')
1341 T = string_to_list_of_solutions(repr(s))
-> 1342 X.extend([t[0] for t in T])
1343 except TypeError as mess:
1344 if ignore_exceptions:
/usr/local/sage-9/local/lib/python3.9/site-packages/sage/symbolic/relation.py in <listcomp>(.0)
1340 s = m.to_poly_solve(x, options='algexact:true')
1341 T = string_to_list_of_solutions(repr(s))
-> 1342 X.extend([t[0] for t in T])
1343 except TypeError as mess:
1344 if ignore_exceptions:
TypeError: 'sage.symbolic.expression.Expression' object is not subscriptable
```

This might be a bug...

HTH,

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Asked: ** 2020-12-23 01:22:04 +0100 **

Seen: **262 times**

Last updated: **Dec 23 '20**

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