Are these triangles congruent? an explanation would be nice

Which logarithmic equation is equivalent to the exponential equation below? e^a=55(you will receive 34 points)

Which of the following is true for the relation f(x)=2x^2+1

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.