Question

What is the solution to the equation below? log 20xrise 3-2logx=4

Answer 1

500

Explanation:

Answer 2

`x = 500`

Explanation:

Given

`log20x^3 - 2logx = 4`

Required

Solve for x

`log20x^3 - 2logx = 4`

Using law of logarithm which says;

`nlogx = logx^n`

The expression becomes

`log20x^3 - logx^2 = 4`

Also, using laws of logarithm which says:

`loga - logb = log(a)/(b)`

The expression becomes

`log((20x^3)/(x^2)) = 4`

`log(20x) = 4`

Also, using laws of logarithm which says

`If\ loga = b\\then\ a = 10^b`

The expression becomes

`20x = 10^4`

`20x = 10000`

Divide through by 20

`(20x)/(20) = (10000)/(20)`

`x = (10000)/(20)`

`x = 500`