What is the solution of equation 6^(y+1)-5*6^y-1=0?

We'll apply change the variable to solve the given
exponential equation.

6^y =
t

We'll express 6^(y+1)=(6^y)*6, based on the property of
multiplying 2 exponential functions, having matching
bases.

The equation will
become:

6*6^y -5*6^y-1 = 0

But
6^y=t:

6t - 5t - 1 = 0

We'll
combine like terms:

t - 1 =
0

We'll add 1 both sides:

t =
1

But 6^y = t=1

We could write
1=6^0

6^y=6^0

The
only possible solution of the given equation is
y=0.