Algebra Examples

\log_{7} (\frac{1}{7})

$\log_{7} (\frac{1}{7})$

Step 1

Rewrite as an equation.

\log_{7} (\frac{1}{7}) = x

$\log_{7} (\frac{1}{7}) = x$

Step 2

Rewrite

\log_{7} (\frac{1}{7}) = x

$\log_{7} (\frac{1}{7}) = x$ in exponential form using the definition of a logarithm. If

x

$x$ and

b

$b$ are positive real numbers and

b

$b$ does not equal

1

$1$ , then

\log_{b} (x) = y

$\log_{b} (x) = y$ is equivalent to

b^{y} = x

$b^{y} = x$ .

7^{x} = \frac{1}{7}

$7^{x} = \frac{1}{7}$

Step 3

Create equivalent expressions in the equation that all have equal bases.

7^{x} = 7^{- 1}

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

Step 4

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

x = - 1

$x = - 1$

Step 5

The variable

x

$x$ is equal to

- 1

$- 1$ .

- 1

$- 1$