Basic Math Examples

$256 = 1^{n - 1}$

Step 1

Rewrite the equation as $1^{n - 1} = 256$ .

$1^{n - 1} = 256$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (1^{n - 1}) = \ln (256)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (1^{n - 1})$ by moving $n - 1$ outside the logarithm.

$(n - 1) \ln (1) = \ln (256)$

Step 3.2

The natural logarithm of $1$ is $0$ .

$(n - 1) \cdot 0 = \ln (256)$

Step 3.3

Multiply $n - 1$ by $0$ .

$0 = \ln (256)$

Step 4

Since $0 \neq \log_{2.71828182} (256)$ , there are no solutions.

No solution

Step 5

Expand the left side.

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Step 5.1

Expand $\ln (1^{n - 1})$ by moving $n - 1$ outside the logarithm.

$(n - 1) \ln (1) = \ln (256)$

Step 5.2

The natural logarithm of $1$ is $0$ .

$(n - 1) \cdot 0 = \ln (256)$

Step 5.3

Multiply $n - 1$ by $0$ .

$0 = \ln (256)$

Step 6

The equation is never true.

No solution