Finite Math Examples

$\log_{b} (1) x + \log_{b} (x - 4) = \log_{b} (1) \cdot 21$

Step 1

Simplify the left side.

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Step 1.1

Simplify each term.

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Step 1.1.1

Logarithm base $b$ of $1$ is $0$ .

$0 x + \log_{b} (x - 4) = \log_{b} (1) \cdot 21$

Step 1.1.2

Multiply $0$ by $x$ .

$0 + \log_{b} (x - 4) = \log_{b} (1) \cdot 21$

Step 1.2

Add $0$ and $\log_{b} (x - 4)$ .

$\log_{b} (x - 4) = \log_{b} (1) \cdot 21$

Step 2

Simplify the right side.

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Step 2.1

Logarithm base $b$ of $1$ is $0$ .

$\log_{b} (x - 4) = 0 \cdot 21$

Step 2.2

Multiply $0$ by $21$ .

$\log_{b} (x - 4) = 0$

Step 3

Rewrite $\log_{b} (x - 4) = 0$ 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 $b^{y} = x$ .

$b^{0} = x - 4$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $x - 4 = b^{0}$ .

$x - 4 = b^{0}$

Step 4.2

Anything raised to $0$ is $1$ .

$x - 4 = 1$

Step 4.3

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

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Step 4.3.1

Add $4$ to both sides of the equation.

$x = 1 + 4$

Step 4.3.2

Add $1$ and $4$ .

$x = 5$