Solve for w natural log of 4w+9=5

$\ln (4 w + 9) = 5$

Step 1

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

$e^{\ln (4 w + 9)} = e^{5}$

Step 2

Rewrite $\ln (4 w + 9) = 5$ 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 $b^{y} = x$ .

$e^{5} = 4 w + 9$

Step 3

Solve for $w$ .

Rewrite the equation as $4 w + 9 = e^{5}$ .

$4 w + 9 = e^{5}$

Subtract $9$ from both sides of the equation.

$4 w = e^{5} - 9$

Divide each term in $4 w = e^{5} - 9$ by $4$ and simplify.

Divide each term in $4 w = e^{5} - 9$ by $4$ .

$\frac{4 w}{4} = \frac{e^{5}}{4} + \frac{- 9}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 w}{4} = \frac{e^{5}}{4} + \frac{- 9}{4}$

Divide $w$ by $1$ .

$w = \frac{e^{5}}{4} + \frac{- 9}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$w = \frac{e^{5}}{4} - \frac{9}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$w = \frac{e^{5}}{4} - \frac{9}{4}$

Decimal Form:

$w = 34.85328977 \dots$

Solve for w natural log of 4w+9=5

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