# What is x if log(7x-10) - 3 log(x)= 2 ?

Nov 29, 2015

Not solved, but got it in the general cubic equation form.

#### Explanation:

Here is my attempt to solve it.
Assuming $\log$ is ${\log}_{10}$:

$\log \left(7 x - 10\right) - 3 \log \left(x\right) = 2$

becomes:

$\log \left(7 x - 10\right) - \log \left({x}^{3}\right) = 2$

$\log \left(\frac{7 x - 10}{{x}^{3}}\right) = 2$

$\frac{7 x - 10}{{x}^{3}} = {10}^{2}$

$7 x - 10 = 100 {x}^{3}$

$100 {x}^{3} - 7 x + 10 = 0$

${x}^{3} - \frac{7}{100} x + \frac{1}{10} = 0$

Here we have the same equation in cubic form.
Then you're on your own to solve this.
It is way too long to describe the calculations here and may involve complex roots (you could first compute the discriminant $\Delta$ to see how many roots it has).