Finite Math Examples

f (x) = ln (x - 1)

$f (x) = \ln (x - 1)$

Step 1

Set

ln (x - 1)

$\ln (x - 1)$ equal to

0

$0$ .

ln (x - 1) = 0

$\ln (x - 1) = 0$

Step 2

Solve for

x

$x$ .

Tap for more steps...

Step 2.1

To solve for

x

$x$ , rewrite the equation using properties of logarithms.

e^{ln (x - 1)} = e^{0}

$e^{\ln (x - 1)} = e^{0}$

Step 2.2

Rewrite

ln (x - 1) = 0

$\ln (x - 1) = 0$ 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

$b^{y} = x$ .

e^{0} = x - 1

$e^{0} = x - 1$

Step 2.3

Solve for

x

$x$ .

Tap for more steps...

Step 2.3.1

Rewrite the equation as

x - 1 = e^{0}

$x - 1 = e^{0}$ .

x - 1 = e^{0}

$x - 1 = e^{0}$

Step 2.3.2

Anything raised to

0

$0$ is

1

$1$ .

x - 1 = 1

$x - 1 = 1$

Step 2.3.3

Move all terms not containing

x

$x$ to the right side of the equation.

Tap for more steps...

Step 2.3.3.1

Add

1

$1$ to both sides of the equation.

x = 1 + 1

$x = 1 + 1$

Step 2.3.3.2

Add

1

$1$ and

1

$1$ .

x = 2

$x = 2$

x = 2

$x = 2$

x = 2

$x = 2$

x = 2

$x = 2$

Step 3