Question

What is the solution to the equation below? riund your answer to two decimal places. (24) log(3x) = 60

Answer 1

The answer is:  " x = 105.41 " . 

_____________________________________________

Explanation:

_____________________________________________

Given:   " 24 log (3x) = 60 " ;  Solve for "x" .

The default is to assume "base 10" for the "logarithm". 

_____________________________________________

Start by dividing each side of the equation by "24" ; 

       →   [ 24 log(3x) ] / 24  = 60 / 24 ; 

to get:  

_____________________________________________

 log (3x)  = 2.5 ;

_____________________________________________

Rewrite as:  log₁₀ (3x) = 2.5 ;  

_____________________________________________

Using the property of logarithms:

⇔    10⁽²·⁵⁾  =   3x  ;  

↔   3x = 10⁽²·⁵⁾   ;

         →  10^ (2.5) = 316.2277660168379332 ;

     →  3x = 316.227766016837933 ;  

Divide each side of the equation by "3" ;

  to isolate "x" on one side of the equation;

      and to solve for "x" ;

    →  3x / 3 =  316.2277660168379332 / 3  ;

to get:

    →   x = 105.4092553389459777333 ;

    →  round to 2 (two) decimal places;

_____________________________________________

         →   " x = 105.41 " .

_____________________________________________

 Hope this helps!

    Best wishes to you!

_____________________________________________