Vbe in the active region of a 2N3904

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Why not let Spice calculate it for you? Run a sim and plot the base voltage.
 
Either extrapolate it from the data sheet information or do a Spice simulation as Alec said.
 
The graphs in a datasheet are for a "typical" transistor that you cannot buy. You might get a transistor with a minimum or maximum Vbe.
Vbe changes with temperature and current.
Usually a transistor has a series emitter resistor and emitter current produces a voltage across it then the base can be fed a voltage then small changes in Vbe do not affect the operation of the transistor.
 
He is from Nepal. Nepal is the 2nd richest (after Brazil) country in Water Resources but we (Nepalese) are facing sometime more than 24 hours power failure in a day and more than 18 hours loadscheding in a day. So probably he is getting 0.0Vbe.
 
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