Solve for x, calculus

1. e^(4x+1)=p

2. log5(nx)=b
that is log base 5

solve each equation for x

1. e^(4x+1)=p

4x+1 =ln p
4x =[ln p] -1 =ln p -ln e =ln (p/e)

x =ln (p/e) / 4

2. log5(nx)=b

nx =5^b

x =5^b / n

1.
e^(4x+1)=p

Putting ln to both sides:
ln(e^(4x+1))=ln(p)

As ln(e^(4x+1))=4x+1

4x+1=ln(p)

x=(ln(p)-1)/4


2.
log5(nx)=b

By definition:
5^b=nx

x=5^b/n

...e^(4x+1)=p
lne^(4x+1)=lnp
.......4x+1=lnp
............-1..-1
............4x=lnp-1
...........-----.--------
.............4.....4
x=(lnp-1)/4

log5(nx)=b
5^b=nx
-----.-----
..n....n
(5^b)/n=x