Algebra Examples

log (2 x) = 3

$\log (2 x) = 3$

Step 1

Rewrite

log (2 x) = 3

$\log (2 x) = 3$ in exponential form using the definition of a logarithm. If

x

$x$ and

b

$b$ are positive real numbers and

b \neq 1

$b \neq 1$ , then

{log}_{b} (x) = y

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

b^{y} = x

$b^{y} = x$ .

10^{3} = 2 x

$10^{3} = 2 x$

Step 2

Solve for

x

$x$ .

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Step 2.1

Rewrite the equation as

2 x = 10^{3}

$2 x = 10^{3}$ .

2 x = 10^{3}

$2 x = 10^{3}$

Step 2.2

Divide each term in

2 x = 10^{3}

$2 x = 10^{3}$ by

2

$2$ and simplify.

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Step 2.2.1

Divide each term in

2 x = 10^{3}

$2 x = 10^{3}$ by

2

$2$ .

\frac{2 x}{2} = \frac{10^{3}}{2}

$\frac{2 x}{2} = \frac{10^{3}}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of

2

$2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{10^{3}}{2}$

Step 2.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{10^{3}}{2}$

$x = \frac{10^{3}}{2}$

$x = \frac{10^{3}}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Raise

$10$ to the power of

$3$ .

$x = \frac{1000}{2}$

Step 2.2.3.2

Divide

$1000$ by

$2$ .

$x = 500$

$x = 500$

$x = 500$

$x = 500$

$\log (2 x) = 3$

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