Precalculus Examples

{log}_{2} (512)

$\log_{2} (512)$

Step 1

Rewrite as an equation.

{log}_{2} (512) = x

$\log_{2} (512) = x$

Step 2

Rewrite

{log}_{2} (512) = x

$\log_{2} (512) = x$ 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

$b^{y} = x$ .

2^{x} = 512

$2^{x} = 512$

Step 3

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

2^{x} = 2^{9}

$2^{x} = 2^{9}$

Step 4

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

x = 9

$x = 9$

Step 5

The variable

x

$x$ is equal to

9

$9$ .

9

$9$

$\log_{2} (512)$

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