Write in Exponential Form log of 4x- log of 12+ square root of x=2

Problem

(log_)(4*x)−(log_)(12)+√(,x)=2

Solution

1. Group the logarithmic terms on one side of the equation by moving the square root term to the other side.

(log_)(4*x)−(log_)(12)=2−√(,x)

2. Apply the quotient rule for logarithms, which states that (log_)(a)−(log_)(b)=(log_)(a/b)

(log_)((4*x)/12)=2−√(,x)

3. Simplify the fraction inside the logarithm by dividing both the numerator and denominator by 4.

(log_)(x/3)=2−√(,x)

4. Convert to exponential form by using the definition of a common logarithm (base 10), where (log_10)(y)=z⇔10=y

x/3=10(2−√(,x))

Final Answer

(log_)(4*x)−(log_)(12)+√(,x)=2⇒x/3=10(2−√(,x))

Want more problems? Check here!