What does x equal if log(7x)=2?

May 17, 2018

$x = \frac{100}{7}$

Explanation:

$\log 7 x = 2$

But $2 = \log 100$ (because ${10}^{2} = 100$) hence

$\log 7 x = \log 100$

By inyectivity of log function we can say that $7 x = 100$

$x = \frac{100}{7}$

This a valid solution because log(7·100/7)=log100=2

May 17, 2018

$x = \frac{100}{7}$

Explanation:

We have ${\log}_{10} \left(7 x\right) = 2$

which can be rewritten as

${10}^{2} = 7 x$

$\implies 100 = 7 x$

Dividing both sides by $7$, we get

$x = \frac{100}{7}$

Hope this helps!