How do you solve -2=log_x (1/100)?

Dec 21, 2015

$x = 10$

Explanation:

$- 2 = {\log}_{x} \left(\frac{1}{100}\right)$

There are many ways you can solve this problem. The best approach is to convert the given equation to exponent form.

Rule : ${\log}_{b} \left(a\right) = k \implies a = {k}^{b}$

Using the rule we can get

${x}^{-} 2 = \frac{1}{100}$
${x}^{-} 2 = \frac{1}{10} ^ 2$
${x}^{-} 2 = {10}^{-} 2$ Rule $\frac{1}{a} ^ m = {a}^{-} m$

$x = 10$ The final answer.

Alternate approach

$- 2 = {\log}_{x} \left(\frac{1}{100}\right)$
$- 2 = {\log}_{x} \left({10}^{-} 2\right)$
$- 2 = - 2 {\log}_{x} \left(10\right)$ Rule $\log {\left(A\right)}^{n} = n \log \left(A\right)$
$1 = {\log}_{x} \left(10\right)$
$x = 10$ because of the rule ${\log}_{a} \left(a\right) = 1$ x has to be 10.