Basic Math Examples

$1 = 5^{y}$

Step 1

Rewrite the equation as $5^{y} = 1$ .

$5^{y} = 1$

Step 2

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

$\ln (5^{y}) = \ln (1)$

Step 3

Expand $\ln (5^{y})$ by moving $y$ outside the logarithm.

$y \ln (5) = \ln (1)$

Step 4

Simplify the right side.

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Step 4.1

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

$y \ln (5) = 0$

Step 5

Divide each term in $y \ln (5) = 0$ by $\ln (5)$ and simplify.

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Step 5.1

Divide each term in $y \ln (5) = 0$ by $\ln (5)$ .

$\frac{y \ln (5)}{\ln (5)} = \frac{0}{\ln (5)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (5)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{y \ln (5)}{\ln (5)} = \frac{0}{\ln (5)}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{\ln (5)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $\ln (5)$ .

$y = 0$