Algebra Examples

$y = \log_{1000000} (10)$

Step 1

Rewrite as an equation.

$y = \log_{1000000} (10) = x$

Step 2

Rewrite $\log_{1000000} (10) = x$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ does not equal $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$y = 1000000^{x} = 10$

Step 3

Create expressions in the equation that all have equal bases.

$y = {(10^{6})}^{x} = 10^{1}$

Step 4

Rewrite ${(10^{6})}^{x}$ as $10^{6 x}$ .

$y = 10^{6 x} = 10^{1}$

Step 5

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$y = 6 x = 1$

Step 6

Solve for $x$ .

$y = x = \frac{1}{6}$

Step 7

The variable $x$ is equal to $\frac{1}{6}$ .

$y = \frac{1}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1}{6}$

Decimal Form:

$y = 0.1\overline{6}$