Precalculus Examples

$a_{n} = 2^{n}$

Step 1

Rewrite the equation as $2^{n} = a_{n}$ .

$2^{n} = a_{n}$

Step 2

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

$\ln (2^{n}) = \ln (a_{n})$

Step 3

Expand $\ln (2^{n})$ by moving $n$ outside the logarithm.

$n \ln (2) = \ln (a_{n})$

Step 4

Divide each term in $n \ln (2) = \ln (a_{n})$ by $\ln (2)$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $n \ln (2) = \ln (a_{n})$ by $\ln (2)$ .

$\frac{n \ln (2)}{\ln (2)} = \frac{\ln (a_{n})}{\ln (2)}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $\ln (2)$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{n \ln (2)}{\ln (2)} = \frac{\ln (a_{n})}{\ln (2)}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{\ln (a_{n})}{\ln (2)}$