Algebra Examples

$y = \ln (7 x)$

Step 1

Rewrite the equation as $\ln (7 x) = y$ .

$\ln (7 x) = y$

Step 2

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

$e^{\ln (7 x)} = e^{y}$

Step 3

Rewrite $\ln (7 x) = y$ 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 $b^{y} = x$ .

$e^{y} = 7 x$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $7 x = e^{y}$ .

$7 x = e^{y}$

Step 4.2

Divide each term in $7 x = e^{y}$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 x = e^{y}$ by $7$ .

$\frac{7 x}{7} = \frac{e^{y}}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{e^{y}}{7}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{e^{y}}{7}$