Respuesta :
Answer:
x = 500.
Step-by-step explanation:
log20x^3 - 2logx = 4
By the laws of logs:
log20x^3 - logx^2 = 4
log(20x^3 / x^2) = 4
20x^3 / x^2 = 10^4
20x = 10,000
x = 10,000 / 20
x = 500.
The solution of the given logarithmic equation is x = 500.
What is a logarithmic equation?
Any equation in the variable x that contains a logarithm is called a logarithmic equation.
Given logarithmic equation
[tex]log20x^{3} -2logx=4[/tex]
Using [tex]mloga=loga^{m}[/tex]
[tex]log20x^{3} -logx^{2}=4[/tex]
Using [tex]loga-logb=log(\frac{a}{b})[/tex]
[tex]\frac{log20x^{3} }{x^{2} }=4[/tex]
[tex]log20x=4[/tex]
[tex]20x=10^{4}[/tex]
[tex]x=\frac{10000}{20}[/tex]
[tex]x=500[/tex]
The solution of the given logarithmic equation is x = 500.
Find out more information about logarithmic equation here
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