Basic Math Examples

$\log_{4} (- 7 z + 127) = 3$

Step 1

Rewrite $\log_{4} (- 7 z + 127) = 3$ 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 $b^{y} = x$ .

$4^{3} = - 7 z + 127$

Step 2

Solve for $z$ .

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Step 2.1

Rewrite the equation as $- 7 z + 127 = 4^{3}$ .

$- 7 z + 127 = 4^{3}$

Step 2.2

Raise $4$ to the power of $3$ .

$- 7 z + 127 = 64$

Step 2.3

Move all terms not containing $z$ to the right side of the equation.

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Step 2.3.1

Subtract $127$ from both sides of the equation.

$- 7 z = 64 - 127$

Step 2.3.2

Subtract $127$ from $64$ .

$- 7 z = - 63$

Step 2.4

Divide each term in $- 7 z = - 63$ by $- 7$ and simplify.

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Step 2.4.1

Divide each term in $- 7 z = - 63$ by $- 7$ .

$\frac{- 7 z}{- 7} = \frac{- 63}{- 7}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 7$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{- 7 z}{- 7} = \frac{- 63}{- 7}$

Step 2.4.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 63}{- 7}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 63$ by $- 7$ .

$z = 9$