Calculus Examples

$\log (\frac{1}{10^{x}})$

Rewrite $\frac{1}{10^{x}}$ as ${(10^{x})}^{- 1}$ .

$\log ({(10^{x})}^{- 1})$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (10^{x \cdot - 1})$

Use logarithm rules to move $x \cdot - 1$ out of the exponent.

$x \cdot - 1 \log (10)$

Move $- 1$ to the left of $x$ .

$- 1 \cdot x \log (10)$

Rewrite $- 1 x$ as $- x$ .

$- x \log (10)$

Logarithm base $10$ of $10$ is $1$ .

$- x \cdot 1$

Multiply $- 1$ by $1$ .

$- x$