Solve for p m*n^p=q

$m \cdot n^{p} = q$

Step 1

Divide each term in $(m \cdot n^{p}) = q$ by $m$ and simplify.

Divide each term in $(m \cdot n^{p}) = q$ by $m$ .

$\frac{(m \cdot n^{p})}{m} = \frac{q}{m}$

Simplify the left side.

Cancel the common factor of $m$ .

Cancel the common factor.

$\frac{m \cdot n^{p}}{m} = \frac{q}{m}$

Divide $n^{p}$ by $1$ .

$n^{p} = \frac{q}{m}$

Step 2

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

$\ln (n^{p}) = \ln (\frac{q}{m})$

Step 3

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

$p \ln (n) = \ln (\frac{q}{m})$

Step 4

Divide each term in $p \ln (n) = \ln (\frac{q}{m})$ by $\ln (n)$ and simplify.

Divide each term in $p \ln (n) = \ln (\frac{q}{m})$ by $\ln (n)$ .

$\frac{p \ln (n)}{\ln (n)} = \frac{\ln (\frac{q}{m})}{\ln (n)}$

Simplify the left side.

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

Cancel the common factor.

$\frac{p \ln (n)}{\ln (n)} = \frac{\ln (\frac{q}{m})}{\ln (n)}$

Divide $p$ by $1$ .

$p = \frac{\ln (\frac{q}{m})}{\ln (n)}$