Solve for x log base x of 75=2

Problem

(log_x)(75)=2

Solution

1. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(a)=c⇔bc=a

x2=75

2. Solve for x by taking the square root of both sides of the equation.

x=√(,75)

3. Simplify the radical by factoring out the largest perfect square, which is 25

x=√(,25⋅3)

x=5√(,3)

4. Verify the base requirements for logarithms, which state that the base x must be positive and not equal to 1 Since 5√(,3)>0 and 5√(,3)≠1 the solution is valid.

x=5√(,3)

Final Answer

(log_x)(75)=2⇒x=5√(,3)

Want more problems? Check here!