3^x=1/81 solve for x

Yes, Mathematician,  that is when you take the log of both sides.

$$\\log3^x=log(1/81)\\ xlog3=log(1/81)\\ x=log(1/81)/log(3)\\$$

$${\frac{{log}_{10}\left({\frac{{\mathtt{1}}}{{\mathtt{81}}}}\right)}{{log}_{10}\left({\mathtt{3}}\right)}} = -{\mathtt{3.999\: \!999\: \!999\: \!999\: \!999\: \!9}}$$

there is a little rounding error - its not a problem but it is more elegant to do it by hand if you can.

Since  81  =  3^4

then:  1/81  =  3^-4

So:     3^x  =  3^-4     --->     x  =  -4

Is there a way to solve without knowing 3^4=81?