Finite Math Examples

97 \cdot \ln (y) = 91

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

Step 1

Solve for

y

$y$ .

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Step 1.1

Divide each term in

97 \cdot \ln (y) = 91

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

97

$97$ and simplify.

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Step 1.1.1

Divide each term in

97 \cdot \ln (y) = 91

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

97

$97$ .

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

$97$ .

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Step 1.1.2.1.1

Cancel the common factor.

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

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

Step 1.1.2.1.2

Divide

\ln (y)

$\ln (y)$ by

1

$1$ .

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

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

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

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

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

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

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

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

Step 1.2

To solve for

y

$y$ , rewrite the equation using properties of logarithms.

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

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

Step 1.3

Rewrite

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

$\ln (y) = \frac{91}{97}$ in exponential form using the definition of a logarithm. If

x

$x$ and

b

$b$ are positive real numbers and

b \neq 1

$b \neq 1$ , then

\log_{b} (x) = y

$\log_{b} (x) = y$ is equivalent to

b^{y} = x

$b^{y} = x$ .

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

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

Step 1.4

Rewrite the equation as

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

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

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

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

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

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

Step 2

Set

91

$91$ equal to

0

$0$ .

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

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

Step 3

Solve for

x

$x$ .

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Step 3.1

Raise

2.71828182

$2.71828182$ to the power of

\frac{91}{97}

$\frac{91}{97}$ .

2.55523534 = 0

$2.55523534 = 0$

Step 3.2

Since

2.55523534 \neq 0

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

No solution