Precalculus Examples

4 + 3 log (2 x) = 16

$4 + 3 \log (2 x) = 16$

Step 1

Move all terms not containing

log (2 x)

$\log (2 x)$ to the right side of the equation.

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Step 1.1

Subtract

4

$4$ from both sides of the equation.

3 log (2 x) = 16 - 4

$3 \log (2 x) = 16 - 4$

Step 1.2

Subtract

4

$4$ from

16

$16$ .

3 log (2 x) = 12

$3 \log (2 x) = 12$

3 log (2 x) = 12

$3 \log (2 x) = 12$

Step 2

Divide each term in

3 log (2 x) = 12

$3 \log (2 x) = 12$ by

3

$3$ and simplify.

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Step 2.1

Divide each term in

3 log (2 x) = 12

$3 \log (2 x) = 12$ by

3

$3$ .

\frac{3 log (2 x)}{3} = \frac{12}{3}

$\frac{3 \log (2 x)}{3} = \frac{12}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

3

$3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 \log (2 x)}{3} = \frac{12}{3}$

Step 2.2.1.2

Divide

$\log (2 x)$ by

$1$ .

$\log (2 x) = \frac{12}{3}$

$\log (2 x) = \frac{12}{3}$

$\log (2 x) = \frac{12}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide

$12$ by

$3$ .

$\log (2 x) = 4$

$\log (2 x) = 4$

$\log (2 x) = 4$

Step 3

Rewrite

$\log (2 x) = 4$ in exponential form using the definition of a logarithm. If

$x$ and

$b$ are positive real numbers and

$b \neq 1$ , then

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

$b^{y} = x$ .

$10^{4} = 2 x$

Step 4

Solve for

$x$ .

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Step 4.1

Rewrite the equation as

$2 x = 10^{4}$ .

$2 x = 10^{4}$

Step 4.2

Divide each term in

$2 x = 10^{4}$ by

$2$ and simplify.

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Step 4.2.1

Divide each term in

$2 x = 10^{4}$ by

$2$ .

$\frac{2 x}{2} = \frac{10^{4}}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

$2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{10^{4}}{2}$

Step 4.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{10^{4}}{2}$

$x = \frac{10^{4}}{2}$

$x = \frac{10^{4}}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Raise

$10$ to the power of

$4$ .

$x = \frac{10000}{2}$

Step 4.2.3.2

Divide

$10000$ by

$2$ .

$x = 5000$

$x = 5000$

$x = 5000$

$x = 5000$

$4 + 3 \log (2 x) = 16$

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