Solve for x: log4^x+log4^(x+1)=7

Does "log4^x" mean "logarithm to the base 4 of x"?
I prefer "log4(x)".

log4(x) + log4(x + 1) = log4(x² + x), which equals 7
Raise 4 to the power of each side:
x² + x = 4^7 = 16384
x² + x - 16384 = 0
x = (-1 ± √(1 + 65536))/2

Or does "log4^x" mean "(common) logarithm of: 4 to the power of x"?
Then it should be log(4^x)
log(4^x) + log(4^(x+1)) = x(log(4)) + (x+1)(log(4)) = 7
(2x + 1)(log(4)) = 7
2x + 1 = 7/(log(4))
2x = 7/(log(4)) - 1
x = 7/[2(log(4))] - ½

log(4^x)+log(4^(x+1))=7
(x+x+1)log(4)=7
2x+1=7/log(4)
x=(7/log(4)-1)/2