Question

What is the solution to this equation? log₆ x + log₆ 3 = log₆ ( x+1) a. x=1/2 b. x=3/2 c. x=1/3 d. x=-1

Answer 1

x = 1/2

Explanation:

the arguments or the logarithm must be positive

x > 0

x + 1 > 0

x > -1

if we match the condition, we have x > 0

We can use a property of logarithms to multiply the arguments of the first member

log₆ (3x) = log₆ (x+1)

Since the base is equal we have only to put equal the arguments

3x = x+1

3x -x = 1

2x = 1

2/2 x = 1/2

x = 1/2