QuantityVariable usage

Question

When I try to run the following code, Mathematica gives me an error message: "Solve was unable to determine the units of quantities that appear in the input."

With[{}, Solve[Quantity[-135, 1/"Hertz"] == 
10 Log10[QuantityVariable["x", 1/"Hertz"]], QuantityVariable["x", 1/"Hertz"]] // Normal]

It turns out the Mathematica does not recognize the (1/Hertz) unit in QuantityVariable["x", 1/("Hertz")]. I get the same error even if I modified the code a bit:

With[{}, Solve[Quantity[-135, "Seconds"] == 10 Log10[QuantityVariable["x", "Seconds"]], QuantityVariable["x", "Seconds"]] // Normal]

Is there a better way to write the previous code for Solve to give a correct answer?

Thanks

Answer 1

your code does not work because

• Your equation is dimensionally wrong, that's why Solve[] can't solve it. You're setting "unit" == Log10["unit"]
• You should use Quantity[] instead of QauntityVariable[], because with QuantityVariable[] you define a physical quantity, not a unit. See http://reference.wolfram.com/language/tutorial/SymbolicCalculationsWithUnits.html

Hope this helps