8. Convert from exponential to logarithmic form (or vise versa). a. 20 = ex+3
b. ex + 4 = 24
c. In(x+1) = 11
d. 2ln(x-3) = 12

Step-by-step explanation:

a). 20 = ⇒ ln 20 = x + 3  

b). + 4 = 24

= 20 ⇒ ln 20 = x

c). = x + 1

d). 2ln(x - 3) = 12 ⇔ ln(x - 3)² = 12

= (x - 3)²

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions