Precalculus Examples

$\log (4 z) = 3$

Step 1

Rewrite $\log (4 z) = 3$ 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 $b^{y} = x$ .

$10^{3} = 4 z$

Step 2

Solve for $z$ .

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Step 2.1

Rewrite the equation as $4 z = 10^{3}$ .

$4 z = 10^{3}$

Step 2.2

Divide each term in $4 z = 10^{3}$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 z = 10^{3}$ by $4$ .

$\frac{4 z}{4} = \frac{10^{3}}{4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 z}{4} = \frac{10^{3}}{4}$

Step 2.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{10^{3}}{4}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Raise $10$ to the power of $3$ .

$z = \frac{1000}{4}$

Step 2.2.3.2

Divide $1000$ by $4$ .

$z = 250$