Question 760450
solve for x

log(x+8)-log(x)=1
{{{log((x+8)/(x))=1=log(10)}}}
(x+8)/x=10
10x=x+8
9x=8
x=8/9
check:
log(x+8)=log(8/9+8)≈0.0.9488
log(x)=log(8/9)≈-0.0511
0.0.9488-(-0.0511)≈0.9999..
..

{{{sqrt (3)^(x+1) = 9^(6x-1)}}}
{{{(3)^((x+1)/2) = 3^(2*(6x-1))}}}
{{{(3)^((x+1)/2) = 3^(12x-2))}}}
((x+1)/2)=12x-2
x+1=24x-4
23x=5
x=5/23 
check:
√(3^(x+1))=√(3^(5/23+1))=√(3^(1.2174))=√3.8093)≈1.9517
9^(6x-1)=9^(30/23-1)=9^0.3043≈1.9517