# How do you solve log_x7 = 1?

Oct 26, 2015

$x = 7$

#### Explanation:

${\log}_{a} \left(b\right) = \ln \frac{b}{\ln} \left(a\right)$

So

${\log}_{x} \left(7\right) = \ln \frac{7}{\ln} \left(x\right)$

$\implies \ln \frac{7}{\ln} \left(x\right) = 1$

$\implies \ln \left(7\right) = \ln \left(x\right)$

Taking exponentiel both side

$\implies x = 7$

Oct 26, 2015

x=7

#### Explanation:

Consider powers of 10
Picking one at random

${10}^{2} = 100$

If this were to be written as log base 10 it would be:

${\log}_{10} \left(100\right) = 2$

Following the same approach for your question but in you case we could reverse the process to get something we can work out.

so ${\log}_{x} \left(7\right) = 1 \text{ "->" } {x}^{1} = 7$

Anything raised to the power of one is its own value

So ${x}^{1} = x = 7$

This means that if z is any number (technically you would have to say that $z \in R$ but I would not wary about that!)

Then ${\log}_{z} \left(z\right) = 1$