Question

7. Solve for x,(3√4)2x+1/2 =1/32​

Answer 1

SOLUTION

Cube root of 4 = 4^1/3

=(cube root of 4)^2x+1/2=4^1/3(2x+1/2)

=) 4^1/3[(4x+1)/2]

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

since, 4= 2^2

=) 4^(4x+1)/6 = 2^2(4x+1)/6

=) 2^(4x+1)/3

Now, 1/32 = 1/2^5

This is in form 1/a^m which is a^-m

=) 2^(4x+1)/3= 2^-5

Since it is two on both sides, we now take the exponents.

=(4x+1)/3= -5

=(4x+1)= -15

=4x= -15-1

=4x= -16

=x= -16/4

x= -4

Hence, x= -4

For verification

2^(4x+1)/3 = 2^[(4×-4)+1]/3

=) 2^-15/3 = 2^-5 which is R.H.S

Therefore, L.H.S = R.H.S

Hope it helps