Logssssssssss?

Question

Solve for x:
1- log2 radical 8 = x
2- (4/3)^x+1=9/16
3- log(2+x)log(x-3)=log14

Yes, sorry was a typo #3 is:
log(2+x)=log(x-3)=log14

my keyboard is spazzing! lol
log(2+x)+(x-3)=log14

Answer 1

Solve for x:
1- log2 radical 8 = x
x is the exponent
2^x = sqrt(8)
2^x = 2^{3/2}
so x = 3/2
2- (4/3)^x+1=9/16
(4/3)^x = -7/16 so it does not have any solutions
3- log(2+x)+ log(x-3)=log14
log( (2+x) (x-3) ) = log 14
(2+x) ( x-3) = 14
x^2 -x -6 = 14
x^2 -x - 20 =0
(x -5)(x+4) =0 so x = 5 or x = -4

Answer 2

1. log_2( sqrt(8))= log_2 2^(3/2) x=3/2
2. (4/3)^(x+1) = (4/3)^(-2)
x + 1 = -2
x = -3

3. is there a +/- between the two logs?