Solve for n (c^4)/(c^4)=c^n

$\frac{c^{4}}{c^{4}} = c^{n}$

Step 1

Rewrite the equation as $c^{n} = \frac{c^{4}}{c^{4}}$ .

$c^{n} = \frac{c^{4}}{c^{4}}$

Step 2

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

$\ln (c^{n}) = \ln (\frac{c^{4}}{c^{4}})$

Step 3

Expand $\ln (c^{n})$ by moving $n$ outside the logarithm.

$n \ln (c) = \ln (\frac{c^{4}}{c^{4}})$

Step 4

Simplify the right side.

Simplify $\ln (\frac{c^{4}}{c^{4}})$ .

Cancel the common factor of $c^{4}$ .

Cancel the common factor.

$n \ln (c) = \ln (\frac{c^{4}}{c^{4}})$

Rewrite the expression.

$n \ln (c) = \ln (1)$

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

$n \ln (c) = 0$

Step 5

Divide each term in $n \ln (c) = 0$ by $\ln (c)$ and simplify.

Divide each term in $n \ln (c) = 0$ by $\ln (c)$ .

$\frac{n \ln (c)}{\ln (c)} = \frac{0}{\ln (c)}$

Simplify the left side.

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

Cancel the common factor.

$\frac{n \ln (c)}{\ln (c)} = \frac{0}{\ln (c)}$

Divide $n$ by $1$ .

$n = \frac{0}{\ln (c)}$

Simplify the right side.

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

$n = 0$