Question

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

Answer 1

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 $x=500.$

Answer 2

Log 20x^3 - 2 log x = 4
log 20x^3 - log x^2 = 4
log (20x^3/x^2) = 4
log 20x = 4
20x = 10,000
x = 500 Answer