How do you solve 7^x=49?

Sep 30, 2016

$x = 2$

Explanation:

${7}^{x} = 49$
$\implies {7}^{x} = {7}^{2}$
$\implies x = 2$

$x = 2$

Explanation:

By observation we can see that $x = 2$ because ${7}^{2} = 49$. But let's solve this another way. We can do it using logs.

${7}^{x} = 49$

$\log {7}^{x} = \log 49$

$x \log 7 = \log \left(7 \times 7\right)$

$x = \log \frac{7 \times 7}{\log} 7$

$x = \frac{\log 7 + \log 7}{\log} 7$

$x = \log \frac{7}{\log} 7 + \log \frac{7}{\log} 7 = 1 + 1 = 2$