If (42)^p = 41^4, what is the value of p?

First you need to make both bases the same:

Lets remove the ^p and ^4

To make the base of 42 equal to 41, you would have 41^x = 41

X - ln(42) / ln(41) = 1.00648904

Now you have 41^1.00648904(p) = 41^4

Now the bases are equal so we need to set the exponents to equal:

1.00648904(p) = 4

Divide both sides by 1.00648904 to solve for P

P = 4 / 1.00648904

P = 3.97421114