What is the exact value of x in the exponential equation 3.2 + e^6x = 54.2?

3.2 + e^(6x) = 54.2      subtract 3.2 from both sides

e^(6x)  = 51     take the LN  of both sides

LN e^(6x)  = LN  51     and we can write

6x LN (e)   = LN 51       and LN = 1 so we can ignore this....and we have...

6x  = LN 51      divide both sides by 6

x = LN (51)  / 6    = about   0.6553