Finite Math Examples

$97 \cdot \ln (y) = 91$

Step 1

Solve for $y$ .

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Step 1.1

Divide each term in $97 \cdot \ln (y) = 91$ by $97$ and simplify.

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Step 1.1.1

Divide each term in $97 \cdot \ln (y) = 91$ by $97$ .

$\frac{97 \cdot \ln (y)}{97} = \frac{91}{97}$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $97$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{97 \cdot \ln (y)}{97} = \frac{91}{97}$

Step 1.1.2.1.2

Divide $\ln (y)$ by $1$ .

$\ln (y) = \frac{91}{97}$

Step 1.2

To solve for $y$ , rewrite the equation using properties of logarithms.

$e^{\ln (y)} = e^{\frac{91}{97}}$

Step 1.3

Rewrite $\ln (y) = \frac{91}{97}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{\frac{91}{97}} = y$

Step 1.4

Rewrite the equation as $y = e^{\frac{91}{97}}$ .

$y = e^{\frac{91}{97}}$

Step 2

Set $91$ equal to $0$ .

$e^{\frac{91}{97}} = 0$

Step 3

Solve for $x$ .

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Step 3.1

Raise $2.71828182$ to the power of $\frac{91}{97}$ .

$2.55523534 = 0$

Step 3.2

Since $2.55523534 \neq 0$ , there are no solutions.

No solution