Mathematics: What is the solution to the equation below? log20x^3-2logx=4

What is the solution to the equation below? log20x^3-2logx=4

Ответ:

koolboy

01.06.2020

To solve the equation $\log_{10}(20x^3)-2\log_{10}(x)=4$ we will need some useful rules for logarithms. The first rule tells us that ,

$2\log_{10}x=\log_{10}x^2....(1)$ .

The second rule tells us that,

$\log_{10}(20x^3)-\log_{10}(x^2)=\log_{10}(\tfrac{20x^3}{x^2})=\log_{10}(20x).$

Lastly, we have to use the definition of the logarithm, i.e

$\log_{a}(x)=b\\=a^b=x.$

With these rules in mind, we can now proceed to solve the equation given in this problem as follows,

$\log_{10}(20x^3)-2\log_{10}(x)=4\\=\log_{10}(20x^3)-\log_{10}(x^2)=4\\=\log_{10}(\frac{20x^3}{x^2})=4\\=\log_{10}(20x)=4\\=20x=10^4=10000\\=x=\frac{10000}{20}=500$

The solution to this equation is x=500.

0,0(0 оценок)

What is the solution to the equation below? log20x^3-2logx=4

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question