Solve for a 8^a=1

$8^{a} = 1$

Step 1

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

$\ln (8^{a}) = \ln (1)$

Step 2

Expand $\ln (8^{a})$ by moving $a$ outside the logarithm.

$a \ln (8) = \ln (1)$

Step 3

Simplify the right side.

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

$a \ln (8) = 0$

Step 4

Divide each term in $a \ln (8) = 0$ by $\ln (8)$ and simplify.

Divide each term in $a \ln (8) = 0$ by $\ln (8)$ .

$\frac{a \ln (8)}{\ln (8)} = \frac{0}{\ln (8)}$

Simplify the left side.

Cancel the common factor of $\ln (8)$ .

Cancel the common factor.

$\frac{a \ln (8)}{\ln (8)} = \frac{0}{\ln (8)}$

Divide $a$ by $1$ .

$a = \frac{0}{\ln (8)}$

Simplify the right side.

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

$a = \frac{0}{\ln (2^{3})}$

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$a = \frac{0}{3 \ln (2)}$

Cancel the common factor of $0$ and $3$ .

Factor $3$ out of $0$ .

$a = \frac{3 (0)}{3 \ln (2)}$

Cancel the common factors.

Factor $3$ out of $3 \ln (2)$ .

$a = \frac{3 (0)}{3 (\ln (2))}$

Cancel the common factor.

$a = \frac{3 \cdot 0}{3 \ln (2)}$

Rewrite the expression.

$a = \frac{0}{\ln (2)}$

Divide $0$ by $\ln (2)$ .

$a = 0$