f = Module[{l}, l = Log[#, ConditionalExpression[#2, #2 > 0]] &; With[{Log = l}, #]]&;
f @ Unevaluated @ Plot[Log[27, Sin[2*x] - 1/3*Cos[x]] - 1/3*Log[3, -Cos[x]], {x, -Pi, Pi}]
Alternatively,
g = ConditionalExpression[#, Simplify[FunctionDomain[#, x] /. C[1] -> 0]]&;
Plot[Evaluate[g@Log[27, Sin[2*x] - 1/3*Cos[x]] - 1/3*Log[3, -Cos[x]]], {x, -Pi, Pi}]
same picture
f = Module[{l}, l = Log[#, ConditionalExpression[#2, #2 > 0]] &; With[{Log = l}, #]]&;
f @ Unevaluated @ Plot[Log[27, Sin[2*x] - 1/3*Cos[x]] - 1/3*Log[3, -Cos[x]], {x, -Pi, Pi}]
f = Module[{l}, l = Log[#, ConditionalExpression[#2, #2 > 0]] &; With[{Log = l}, #]]&;
f @ Unevaluated @ Plot[Log[27, Sin[2*x] - 1/3*Cos[x]] - 1/3*Log[3, -Cos[x]], {x, -Pi, Pi}]
Alternatively,
g = ConditionalExpression[#, Simplify[FunctionDomain[#, x] /. C[1] -> 0]]&;
Plot[Evaluate[g@Log[27, Sin[2*x] - 1/3*Cos[x]] - 1/3*Log[3, -Cos[x]]], {x, -Pi, Pi}]
same picture
Plot[Log[27f = Module[{l}, ConditionalExpression[#l = Log[#, #ConditionalExpression[#2, #2 > 0]0]] &@(Sin[2*x]&; -With[{Log 1/3*Cos[x])]= -l}, #]]&;
f @ Unevaluated 1/3*Log[3,@ ConditionalExpression[#Plot[Log[27, #Sin[2*x] >- 0]1/3*Cos[x]] &- (1/3*Log[3, -Cos[x])]Cos[x]],
{x, -Pi, Pi}]
Plot[Log[27, ConditionalExpression[#, # > 0] &@(Sin[2*x] - 1/3*Cos[x])] -
1/3*Log[3, ConditionalExpression[#, # > 0] & (-Cos[x])],
{x, -Pi, Pi}]
f = Module[{l}, l = Log[#, ConditionalExpression[#2, #2 > 0]] &; With[{Log = l}, #]]&;
f @ Unevaluated @ Plot[Log[27, Sin[2*x] - 1/3*Cos[x]] - 1/3*Log[3, -Cos[x]], {x, -Pi, Pi}]