Basic Math Examples

$2 = 1^{0.015 y}$

Step 1

Rewrite the equation as $1^{0.015 y} = 2$ .

$1^{0.015 y} = 2$

Step 2

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

$\ln (1^{0.015 y}) = \ln (2)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (1^{0.015 y})$ by moving $0.015 y$ outside the logarithm.

$0.015 y \ln (1) = \ln (2)$

Step 3.2

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

$0.015 y \cdot 0 = \ln (2)$

Step 3.3

Multiply $0$ by $0.015$ .

$0 y = \ln (2)$

Step 3.4

Multiply $0$ by $y$ .

$0 = \ln (2)$

Step 4

Since $0 \neq \log_{2.71828182} (2)$ , there are no solutions.

No solution

Step 5

Expand the left side.

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Step 5.1

Expand $\ln (1^{0.015 y})$ by moving $0.015 y$ outside the logarithm.

$0.015 y \ln (1) = \ln (2)$

Step 5.2

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

$0.015 y \cdot 0 = \ln (2)$

Step 5.3

Multiply $0$ by $0.015$ .

$0 y = \ln (2)$

Step 5.4

Multiply $0$ by $y$ .

$0 = \ln (2)$

Step 6

The equation is never true.

No solution