Solve for x algebraically Give exact solutions where necessa

Solve for x algebraically, Give exact solutions, where necessary,

a. 8 = 4^x^2 (4 is to the power of x squared (x^2)) multiplied by 2^5x

b. 9^x + 4 multiplied by 3^x - 3 = 0

c. log6 (x+3) + log6 (x+4) = 1

a) 8 = (4^x^2).(2^5x)

2^3 = (2^2x^2).(2^5x)

2^3 = (2^(2x^2 +5x))

3 = 2x^2 +5x

2x^2 +5x -3=0

2x^2 +6x-x -3=0

2x(x+3) -1(x+3)=0

(2x-1) (x+3) =0

so x=1/2 or x=-3

b).

(9^x +4).(3^x -3)=0

so (9^x +4) =0 or (3^x -3)=0

3^x =3

xlog3 =log3

x =1 is solution

c).

log6 (x+3) + log6 (x+4) = 1

log6 (x+3)(x+4) =1

(x+3)(x+4) =6^1

(x^2 +7x +12 =6

x^2 +7x+6=0

x^2+6x+x+6=0

x(x+6) +1(x+6) =0

(x+6)(x+1) =0

so x =-6 or x=-1

but x=-1 we get sloution