Question

What is the true solution to the logarithmic equation below?

log₂ (6x)-log₂ + (√x)=2

O x=0
O x = 1/10
O x = 4
O x = 9

Answer 1

The true solution to the logarithmic equation is x = 9.

Step-by-step explanation:

To solve the logarithmic equation, we need to combine the logarithms on the left side of the equation using the property of logarithms: log(a) - log(b) = log(a/b). Applying this property to the equation, we have:

log₂ (6x/√x) = 2

Simplifying the expression inside the logarithm:

log₂ (6√x) = 2

To eliminate the logarithm, we rewrite the equation as an exponential equation:

2 = 6√x

9 = x

Therefore, the true solution to the logarithmic equation is x = 9.