Solve the following equation: (log (base 10) (x))^2= 3 log (base 10) (x)

Question

Solve the following equations:

 

1) (log (base 10) (x))^2= 3 log (base 10) (x)

2) (log (base 5) (x))^2= 2 log (base 5) (x)

Answer 1

1)

 

(log₁₀(x))² = 3log₁₀(x)

 

 

Divide both sides of the equation by log₁₀(x).

 

log₁₀(x) = 3

 

 

The solution to a logarithm is the exponent of the base number 10.

 

10³ = x

 

1000 = x

 

 

 

Do the same for the second question.