Solve for r x^r-1915=269

$x^{r} - 1915 = 269$

Move all terms not containing $r$ to the right side of the equation.

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Add $1915$ to both sides of the equation.

$x^{r} = 269 + 1915$

Add $269$ and $1915$ .

$x^{r} = 2184$

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

$\ln (x^{r}) = \ln (2184)$

Expand $\ln (x^{r})$ by moving $r$ outside the logarithm.

$r \ln (x) = \ln (2184)$

Divide each term by $\ln (x)$ and simplify.

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Divide each term in $r \ln (x) = \ln (2184)$ by $\ln (x)$ .

$\frac{r \ln (x)}{\ln (x)} = \frac{\ln (2184)}{\ln (x)}$

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

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Cancel the common factor.

$\frac{r \ln (x)}{\ln (x)} = \frac{\ln (2184)}{\ln (x)}$

Divide $r$ by $1$ .

$r = \frac{\ln (2184)}{\ln (x)}$

Solve for r x^r-1915=269

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