Solve the following equations for x
(i)`7^(2x+3)=1`
(ii)`2^(x+1)=4^x`
(iii)`2^(5x+3)=8^(x+3)`

Solve the following equations: 2^(x-5)=256 (ii) 2^(x+3)=4^(x-1)

Solve the following equations for x:4^(2x)=(1)/(32)( ii) 4^(x-1)x(0.5)^(3-2x)=((1)/(8))^(x)2^(3x-7)=256

Solve for following equations for x:(i)5^(2x+3)=1(ii)(sqrt((3)/(5)))^(x+1)=(125)/(27)

Solve the following equation. (x+1)/4+(x+2)/2=(x-3)/2+(x-1)/3

Solve the following equations (i) sgn({[x]})=0 (ii) sgn(x^(2)-2x-8)=-1 (iii)sgn((x^(2)-5x+4)/({x}))=-1

Solve the following equations : (i) log_(x)(4x-3)=2 (ii) log_2)(x-1)+log_(2)(x-3)=3 (iii) log_(2)(log_(8)(x^(2)-1))=0 (iv) 4^(log_(2)x)-2x-3=0

Find the value of x in each of the following cases : (i) 3^(2x+3)=1" "(ii)2^(x-5)xx5^(x-4)=5 (iii)2^(2x+1)=2^(2x-1)+12" "(vi)3^(2x-3)=3sqrt(3)

Solve the following equations: (i) 3^(x+1)=27 xx 3^4 (ii)4^(2x)=(16 3)^(-6/y)=(sqrt(8))^2 (iii) 3^(x-1) xx 5^(2y-3)=225 (iv) 8^(x+1)=16^(x+2) and, (v) (1/2)^(3+x)=(1/4)^(3y) 4^(x-1) xx (0. 5)^(3-2x)=(1/8)^x sqrt(a/b)=(b/a)^(1-2x ) , where a , b are distinct positive primes.

Solve the following equations : (i) |x^(2)-2| = 2 |x-3| (ii) |x^(2)-4|+|x^(2)-9|=0 (iii) |x-1|+|x+5| = 6