Basic Math Examples

$1^{y} = 10$

Step 1

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

$\ln (1^{y}) = \ln (10)$

Step 2

Expand the left side.

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Step 2.1

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

$y \ln (1) = \ln (10)$

Step 2.2

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

$y \cdot 0 = \ln (10)$

Step 2.3

Multiply $y$ by $0$ .

$0 = \ln (10)$

Step 3

Since $0 \neq \log_{2.71828182} (10)$ , there are no solutions.

No solution

Step 4

Expand the left side.

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Step 4.1

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

$y \ln (1) = \ln (10)$

Step 4.2

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

$y \cdot 0 = \ln (10)$

Step 4.3

Multiply $y$ by $0$ .

$0 = \ln (10)$

Step 5

The equation is never true.

No solution